Quantitative Techniques of Business (QTB Report Saydon Pharma)

Quantitative Techniques of Business

Quantitative TechniquesFor

Business

SUBMITTED TO:

Sir Noor Muhammad

HND BUSINESS

SUBMITTED BY:

Sayed Muhammad Ali

DATE: 15th June, 2009


Assessment Brief________________________________________________

1. Unit and Assessment Details

Course Title: HND BusinessUnit Name: Quantitative Techniques for BusinessAssessor: Prof. Noor Muhammad KhanInternal Verifier: Ms.Sadaf Ijaz

Assessment Title: Use of statistical techniques to collect and analyze data, Production of forecasts based on formalized procedures and application of quantitative techniques to business situations. Assessment Method: Report, Viva Voce Assessing in: Group of 2Number of Words: 3000 words (Total 25 Pages Maximum)Outcomes Covered: 1, 2Weightage: Report: 50% Viva Voce: 20%Issue Date: 20/04/09Due Date: 15/06/09

Group Members

College No. Learner Name Responsibilities Learner Signature

7190 Sayed Muhammand AliP1, M1, D1, M2, M3, P4, M4, D2, D3, M5, D4

7202 Muhammad Haris P2, P3, P5

Learner’s Declaration: I confirm that the work submitted for this assignment is my own.

Date : 15th June 2009

Outcomes Covered:

OUTCOME1 Using statistical techniques to collect and analyze data2 Produce forecasts based on formalized methods3 Apply quantitative techniques to business situations


Table of Contents Page

List of Illustration

Synopsis

Introduction................................................................................................................... 01

Outcome-1

Scenario and Task.……..………………………………………………………… 02

Preparation of Plan For Collecting Primary &Secondary Data.…………….... 03

Method Of Collecting Primary Data…....…………………………………...…... 04

Method Of Collecting Secondary Data...………………………………………… 04

Sampling................................................................................................................... 05

Collection of Primary Data About The Sales & Profit Of Saydon Pharma.….. 07

Stake Holders Questionnaire…………..………....………………………….…… 08

Sampling Method For Our Report...……………………………………...…....... 11

Classification of Data....………………………………………………………....... 12

6 Years Sales & Profit of Saydon Pharma……………………………………..... 13

Graph of Sales & Profits Of Saydon Pharma.…………………………….…........ 14

Frequency Distribution………………………………………………………….... 15

Graphs of Frequency Distribution……………………………………………….. 15


Statistical Quantities……………………………………………………………….. 17

Frequency Distribution from Raw Data………………………………………..... 18

Frequency Distribution Techniques for Profits of Saydon Pharma………….... 19

Mean, Median & Mode of Numbers of Sales of Saydon Pharma….………….. 20

Mode, Model Class……………………………………………………..…………. 21

Analysis of the Statistical Quantities…………………………………………....... 24

Outcome-2

Forecasting ………………………………………………...……...……………….. 24

Formalized Methods of Forecasting...………………………….…………………. 25

Comparison on Different Formalized Method of Forecasting…………………. 27

Choosing the Right Forecasting Methodology…………………………………… 33

Reliability of Forecasts………………………………….…………………….…… 34

Assessment and Justification of Forecasted Result………………………………. 35

Conclusion………………………………………………………………………….. 36

Reference List…………………………………………………………………………… 37

Questionnaire……………………………………………………………………………. 38

Minutes of meetings …………………………………………………………………….. 39


Synopsis

This report is prepared for studying sales and profits of Saydon Pharma before and after mergence with Roryan Pharma. We used statistical techniques for collection and analysis of our data and producing forecasts based on the formalized procedure and then the application of quantitative techniques to the business problem. In this report we covered two different aspects concerned with quantitative technique for business.

In the first outcome, we carried out analysis on statistical techniques which include preparation of primary and secondary data, followed by solving a business problem using statistical quantities from frequency distribution.

Second outcome was about the formalized method of forecasting, in this outcome we discussed methods of forecasting and then assessed the reliability of the forecasts made.

In the end, a brief conclusion is given which summarizes our report.


Introduction

This assignment was given by Sir Noor Muhammad teacher for the subject Quantitative Techniques for Business (HND business, semester 2) to our group which comprises of Sayed Muhammad Ali and Muhammad Haris. We were given the task for submission of report on the statistical techniques and formalized method of forecasting to business situation. 15th June, 2009 was given as a last date for the completion of this assignment. For this purpose, we selected Saydon Pharmaceutical Company of national and international level.Saydon Pharmaceutical Company is one of the local pharmaceutical companies in a private sector, based in industrial estate Hayatabad, Peshawar. This company was started in April 1996 by three real brothers and one first cousin. All of them had good experience of dealing in medicines because formally they were jointly running medicine business by the name of Lahore Medicine Company in the Peshawar market, having distribution of renowned national & multinational medicine companies.In the beginning, Saydon were manufacturing only three products and were dealing within the country but now they have expanded their business and have 121 medicines registered with the ministry of health, Islamabad. Out of this list 45 products are being manufactured and exported to outside countries like Afghanistan, Burma and Srilanka etc.In the year 2007, mergence of Roryan Pharma took placed with Saydon Pharma.In order to get clearer concepts regarding statistical techniques and getting primary and secondary data, we visited Saydon Pharma. Interviews were conducted of the higher authorities, which helped us a lot to come up with comprehensive analysis and preparing our report on the said Pharmaceutical Company. A questionnaire was prepared for the interview, which is attached as an annexure to the report.

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Scenario and Task:

The owner of Saydon Pharmaceutical became investor and partner in another pharmaceutical company named Roryan Pharma which was newly started. But this expansion in their business adversely affected Saydon Pharma. There was decline in their business and they were compelled to think over it. For which they consulted a consultant to evaluate the position of these two pharmaceutical companies in the market. The task was given to Sayed Muhammad Ali & Mr. Muhammad Haris the internees of this consultancy.

We proceeded with this task by collecting some primary data and then we obtained secondary data about the sales and profits of the two companies which was already available with them.

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Data:Data is defined as purposefully and systematically collected sets of information or observation. Before discussing the plan regarding collection of primary and secondary data, first primary and secondary data are being defined.Primary data is a data which is collected from the primary source or collected for the first time and not organized numerically. The primary data does not exist already; a person can collect the data for the first time by him/herself. The important point regarding primary data is the uniqueness of data and no one can access it. The main disadvantage of primary data is that, it is time consuming and very costly.Secondary data is a data which has already been collected by someone else for a different purpose (e.g. research study, survey, interview etc). Or in other words we can say that when statistical method applied on primary data they lose their shape and become secondary data. Normally we take secondary data before the primary data because in some cases, the secondary data itself may be sufficient to solve the problem, as there is a probability that some of the questions have been already answered by other investigators or authors.The main advantage of Secondary data is its easy accessibility and also the cost of gathering, which is much lower than the cost of organizing primary data. The main disadvantage of secondary data is its reliability, because a person (researcher) cannot personally check the data so its reliability may be questioned.

Preparation of Plan for Collecting Primary & Secondary Data:The task of data collection begins after problem has been identified. Before deciding about the method of data collection, there are many crucial steps involved in the process which ensures the reliability of the data. A proper plan is made which helps in the smooth operation of data collection. There are three phases involved in the planning of data collection procedure.Pre-Data Collection Phase:1. Goal and Objectives:The goals and objectives of the data collection should be very clear before going into the other details.2. Methodology:Proper methodology should be observed for collection of data i.e. proper observation should be made for the collection of primary data and secondary data. Before going into observation proper knowledge should be acquired about the project and should also know the data analysis technique.3. Ensure Data Collection:Ensuring data is important to avoid errors and repetition. For this a proper plan should be made which will check and verify the data that there is no repetition and the collected data is accurate and authentic.During Data Collection Phase:4. Process:After identifying the three steps of data collection now it is time to act upon them one by one for data collection.Post Data Collection Phase:5. Review:In this phase, result obtained, should be reviewed in order to eliminate irrelevant data.

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Methods of Collecting Primary Data:• Direct Personal Observation: In this method the investigator collects the information

directly from the source available. The person who is collecting the data must be a sharp observer. He/She should ask some simple and easy questions in simple language which could be answer easily.

• Indirect Personal Observation: In this method the investigator collects the information indirectly because direct source of information do not exist or difficult to explain answer. E.g. questions about the income. Thus the reliability of data depends upon the ability of data collector.

• Information though Local Agencies and Correspondents: In this method the investigator or agencies appoints local representatives. Agents and correspondents are sent with due instructions to collect information. This method is costly as compared to the first two methods.

• Questionnaire method: This method involves personal interviews, telephonic interviews and postal surveys. While designing a questionnaire, a firm must set a proper balanced between closed and open ended questions & the questions must simple, short and interesting.

• Personal Interviews: In this method an investigator conducts face to face interview. A main advantage of personal interview is that it gives a collection of in-depth information which concerns them. And the disadvantage of Personal interview is that it takes a lot of time.

• Telephonic Interviews: In this method an investigator conducts the interview over the phone. It is cheaper than conducting a personal interview and also covers a huge area in short period of time.

• Postal Survey: In this method a standard list of questions is sent to the informants by mail or internet, requesting them to return it back to the investigator after answering the given questions. Though it is a cheaper method as compared to any other method mentioned above but response rate of such questionnaires are very low.

Methods of Collecting Secondary Data:Secondary data may exist in the form of business documents or other published data which may include the following.

• Annual Reports & Financial statements of the businesses• Technical and trade journals• Books magazines and newspapers• Banks, stocks exchanges• Reports prepared by various scholars, universities & economists etc• Media (TV, cable and internet etc) are nowadays quite often conducting various kinds of

surveys, which can be utilized.

(BTEC, 2001, pg. 53, 54)

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Sampling:Once the methods and sources are selected then in the next step sampling is being done. Sample is a subset or part of population. Some of the items are drawn from population and these items will represent "population".Sampling is important because it helps in the summarization of a large group. The basic purpose of sampling is to provide an estimate about a population parameter based on sample evidence. In other words the data are selected from some longer set of data whose characteristics we wish to estimate. We call this selection process sampling. There are basically three methods of sampling.Random SamplingQuasi-Random SamplingNon-Random Sampling

1. Random Sampling:In random sampling, each individual or item of the population has an equal chance of being chosen at each draw and the manner of selection should not prefer one individual against the other. For example, a sample of 6 numbers is randomly generated from a population of 45, with each number having an equal chance of being selected.There are basically two methods through which a random sample can be selected.• Lottery method• Using Random number table

2. Quasi-Random Sampling: The main methods of quasi-random sampling are as follow:Systemic samplingStratified samplingMultistage sampling

Systematic Sampling:Systematic sampling, sometimes called interval sampling, means that there is a gap, or interval, between each selection. If systematic sampling approach is selected for generating a sample from a population then all the items of a population are arranged and numbered from 1 to N. After this a random start in which every Kth member is included in the sample. Kth stands for the whole and is the ratio of the population size to sample size. K=N/nE.g. if a systematic sample of 500 students were to be carried out in a university with an enrolled population of 10,000, the sampling interval would be: I = N/n = 10,000/500 =20

Stratified Sampling:In stratified sampling, the population is divided into groups called strata. A sample is then drawn from within these strata. Some examples of strata commonly used by the ABS are States, Age and Sex. Other strata may be religion, academic ability or marital status. On of the method through which a stratified sample can be is selected is as follow:ni = n*Ni/N

ni= represent the sample size of the ith stratum.

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Multistage Sampling: In multistage sampling method, a sample is selected in various stages. First a population is divided into various groups and then randomly selected. Then the selected group is further divided and again randomly selected. This process is continued until the desired sample is achieved. The main advantage of this kind of sampling is no need taking complete random sample, which reduces cost and time.

3. Non-Random Sampling:In a non-random sample, members are selected on the basis of a particular set of characteristics, rather than a random chance of being included. There are two methods through which non-random sampling can be done.• Cluster sampling• Quota sampling

Cluster Sampling:Some times there is a natural grouping of a population; these natural groups are called clusters. According to cluster sampling, we select cluster at random. Cluster must be mutually exclusive and together, the clusters must include the entire population. After clusters are selected, then all units within the clusters are selected. When all the units within a cluster are selected, the technique is referred to as one-stage cluster sampling. If a subset of units is selected randomly from each selected cluster, it is called two-stage cluster sampling. And if it is made in three or more stages then it referred to multistage cluster sampling.

Quota Sampling:According to the quota sampling method, a population is divided into different specific groups and the investigator is told that how much is to be selected from each specified group but is given no specific instruction that how to fulfill his quota while locating them. This type of sampling is done while finding the opinion of public regarding various issues and in various market researches. Though it is a cheaper method but there is danger of becoming biased, as we ignore all those who are out of the survey area or who do not wants to answer the questions.

(BTEC, 2001)

(Encyclopedia, Date Accessed 05/06/2009)

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Plan for the Collection of Primary Data about the Sales and Profits of the Saydon Pharmaceutical Company:

Questionnaire:

First of all our group conducted personal interviews of the directors for getting acquaintance with their problems and then conducted a survey based on the problem of no increase in their profits with lot of investment in Roryan Pharma.. They wanted to know whether they should continue with this new partnership or to withdraw. A questionnaire (see annexure) was prepared for two groups, one for the directors of the company and the second for the stakeholders like doctors (who prescribe their medicines to the patients) and the promotional team of their products. The directors specially finance, production and marketing were consulted and interview for the given problem. We asked two open ended questions from them, one regarding their investment in Roryan and second regarding their expectations about sales and profits.

Questionnaire for Directors of the Company:

Q.No-1: What was the reason that instead of making further investment in Saydon Pharma you preferred to make investment in another pharmaceutical company of the same status?This question was open ended question; every director had his own version. The finance and marketing department were mostly of the opinion that starting joint venture with the Roryan Pharma would almost double their sales and profit margin. As the efforts from both sides would be sufficient to give them boost in production and as well as in their sales, which would naturally increase their profit.On the other hand, production director was of the opinion that this step was very much necessary because the production sector of Saydon Pharma was already over burdened, so instead of making further expansion in the same company would not given us the required result. Therefore the partnership with Roryan Pharma was a good step in a sense that it increases their assets and also the production problem was solved.

Q.No-2: Your profit from Roryan is not according to your expectation & satisfaction, would you like to make further investment for obtaining the required result?Again this is an open-ended question; the answer to the question given by different directors was very much contrasting. The finance director was of the opinion that no further investment should be made, as it has shown no increase in profits rather it has put them under financial stressed and diverted their attention from Saydon Pharma. On the other hand, marketing director was also very much confused about the promotion of the same products of the two companies in the same market, whereas production director was happy with the situation, as they have released from the stress of production.

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Stake Holder Questionnaire:The stakeholder questionnaire consisted of four questions, which involved three close ended questions and one open ended question. The purpose of preparing short questionnaire was to know the opinion of doctors and promotional team. It was obvious that if the questionnaire was made lengthy then no one would have given proper attention to it or simply ignored it.

The contents of the questionnaire were based on what doctors and promotional teams think about the new step of merging of Saydon with Roryan Pharma and whether the merging step was right or wrong, and had it proved a step in the improvement of their products quality? Whether this step has created any problem for them, if not then how much are you hopeful of the betterment of this deed in the near future? As the questionnaire was very straight forward and concerned to them therefore we received a good response from the doctors as well as from the promotional teams.

The questionnaires were divided as follow.

Groups No.sDoctors 20Medical reps. (Zone1)(Abbotabad, Haripur, Mansehra)

10

Medical reps. (Zone2)(Peshawar, Mardan, Swat etc)

15

Medical reps. (Zone3)(Kohat, Bannu, D.I.Khan)

10

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Q.No-1: Do you think that the Merging of Saydon Pharma with Roryan was a Good Step for Success?Out of the total 55 distributed questionnaire we received 48, in which 11 people thought it was a good step whereas 37 people thought it was not. As it is a close ended question so no explanation is given.

Q.No-2: Do you think that this Expansion had proved a Good Step in the Improvement of Their Quality?Out of total 48 questionnaires which were responded, 15 people thought by merging they improved their quality while 33 people thought they have not improved, it’s still the same. Again this was a closed ended question therefore no explanation is given.

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Q.No-3: What are the Problems which you are facing with this step of Merging of Saydon Pharma?This was an open ended question so every individual has its own views. Some doctors believed that the mergence of two companies resulted in giving little attention towards promotion of their products, as the competition between the two companies have totally been finished and the other pharmaceutical companies benefited from this situation. So their sincere opinion was against the mergence of two pharmaceutical companies while some doctors were totally against, as they were of the opinion that this has affected the standard of Saydon Pharma.

On the other hand, there was a contrasting opinion of the promotional teams of different zones. The promotional team of zone 2 (Peshawar, Mardan, Charsada, Swabi & Swat) were quiet happy with this mergence because their zone was larger then other zone and they were alsways under financial stress but now their funds were almost doubled for the same work. They have relieved of such stresses and now they can work openly. While the team of other two zones i.e. zone 1 and zone 3 were not happy with this act of mergence because their zones were not having capability of increasing their sales beyond certain limits due to backwardness of people of those areas.

Q.No-4: Are you Hopeful that this step of Saydon Pharma will prove better in the Future?Out of total 48 questionnaires which were responded, 18 people are hopeful in near future that this step will prove better while 30 people disagreed about the better future of Saydon Pharma. Again this was a closed ended question therefore no explanation is given.

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Sampling Method for Our Report:As it was not practicable to interview each and every member of the two organizations for collection of data, so we confined ourselves to non-random sampling method of study for our problem. For this purpose quota sampling was given due consideration rather than random sampling.

The NWFP was already divided into three zones by the administration of Saydon Pharma which helps us to cover whole NWFP in parts and more accurately i.e.Zone 1 which comprises of Abbotabad, Haripur, Mansehra.Zone 2 which comprises of Peshawar, Mardan, Charsada, Swabi & Swat.Zone 3 which comprises of Kohat, Bannu, D.I.Khan.

In each zone sampling was carried out independently. The doctors and the members of promotional teams which represent a group of segment sharing some characteristics. E.g. Out of many doctors, only those who were already prescribing the medicines of the two Pharmaceutical companies was selected for interviews. Similarly quota sampling was made for interviewing the promotional team of three different zones of NWFP. From each zone few members like zonal managers were selected for interview purpose.

The division of area for distributing the questionnaire and to know the opinion of doctors and promotional team about the sales and profits of Saydon Pharma is as follow:

Groups No.sDoctors 20Medical reps. (Zone1)(Abbotabad, Haripur, Mansehra)

10

Medical reps. (Zone2)(Peshawar, Mardan, Swat etc)

15

Medical reps. (Zone3)(Kohat, Bannu, D.I.Khan)

10

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Classification of data:Numerical information about any thing is called data. Data collected are not directly useful for tabulation. For this the classification of data is essential. The aim of classification is to arrange data systematically for quick and easy understanding or analysis. Data can be classified by two types. i-e Quantitative data and qualitative data.

Quantitative data:The information that can count or expressed numerically is called quantitative data. Quantitative data can be represented by tables, graphs and charts. It generally deals with numbers. Quantitative data are measurable, it can easily be measured. A general description includes facts, figures and scientific observation that can be statistically analyzed and then can be reduced to something that can be enumerated. Quantitative data is often classified as being real. Quantitative are concern with length, height, area, volume, weight, speed, time, temperature, cost, members, ages etc.There are two types of quantitative data.• Discrete• ContinuousDiscrete:Discrete data is that kind of data whose each numerical value has a separate number and there is a gap between one value and next. Discrete data represent a count data (0, 1, 2, 3……….....). E.g. Number of children in family, Number of rooms in a house etc.Continuous:Continuous data is that kind of data which can take all possible values in interval. A continuous data represent measurement data e.g. age of a person, temperature, thermometer etc.

Example:Let’s take the example of quantitative data. If we have a painting picture of a beautiful scene then the quantitative data describes this picture in this way.Picture is 12" by 16"With frame 16" by 20"Weighs 9.5 poundsSurface area of painting is 160sq. inCost 1000 RS.

Qualitative data: The data which deals with description is called qualitative data. Qualitative data expressed in terms of quality. Qualitative research is based on individual. A general description of properties that can not be written in numbers is called qualitative data. A qualitative data can be observed but can not measurable. As the name indicates that this type of data concern with quality. This type of data used as a method of labeling and identifying e.g. intelligence, skin, eye colors, textures, smells, beauty etc.Example:Let’s take the same example of quantitative data that we have painting picture of a beautiful scene then the qualitative data describes this picture in this way. The color of the frame is red. There are three colors used in this painting i.e. grey, white green and blue. The textures shows brush strokes of oil paint. The picture shows the peaceful scene of the country.

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Six (6) Years Sales and Profits of Saydon Pharma:

Half Year (6 months) Saydon Sales (In Million

Rupees)

Roryan Sales (In Million

Rupees)

Total Sales of Saydon after merging with

Roryan Pharma (In

Million)

Total Profit of Saydon

Pharma (In Million Rupees)

Total Profit percentage of

Saydon Pharma

1 Jan - 30 June 2003 60 - 60 12 20

1 July - 31 Dec 2003 62 - 62 12.4 20

1 Jan - 30 June 2004 72 - 72 18 25

1 July - 31 Dec 2004 65 - 65 16.25 25

1 Jan - 30 June 2005 76 - 76 19 25

1 July - 31 Dec 2005 77 - 77 19.25 25

1 Jan - 30 June 2006 76 - 76 22.8 30

1 July - 31 Dec 2006 80 - 80 24 30

1 Jan - 30 June 2007 70 23 93 18.6 20

1 July - 31 Dec 2007 72 25 97 19.4 20

1 Jan - 30 June 2008 70 23 93 18.6 20

1 July - 31 Dec 2008 70 25 95 19 20

Analysis:This data was collected from the account section of Saydon Pharma. They have arranged their sales and profits on half yearly basis. Their normal profit on the sale is at the rate of 35% but the variation in the net profit is the result of incurring expenses in the new venture. As shown in the table, the industry was blooming in the first four years but after getting new partnership with Roryan Pharma, they were expecting increase in their profits but on contrary there was a down fall in the graph of their profit rate. Apparently their total sales increased from 80 to 97 millions but the ratio of the profit margin decreased by 10%.

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Frequency Distribution:A table containing numerical information along with their respective frequencies is called frequency distribution. Or in other words we can say that a large number of data who possesses different characteristics is grouped into different classes. Then observations are determined in each class. The arrangement of these classes into tabular form makes frequency distribution. The number of observations falling in a class makes a class frequency.

A frequency distribution shows the number of observation falling into each of several ranges of values. Frequency distributions can show either the actual number of observations falling in each range or the percentage of observations. In order to present a frequency distribution graphically the following methods are used i.e. frequency curve, histograms, polygons, and ogive.

Graphs of Frequency Distribution:

Frequency Curve:A frequency curve is a smooth free hand curve .It is drawn through the vertices of a frequency polygon. For constructing a smoothed frequency curve, it is necessary to construct a frequency polygon first. In frequency curve class marks on x-axis and frequency marks on y-axis.

Histogram:A histogram is a method of presenting a frequency distribution in visual form. It is constructing by creating or adjoining the rectangles whose widths are the intervals and whose heights represent the frequency. The class boundaries are shown on x-axis and rectangles are constructed width proportional to class intervals size and heights proportional to class frequencies.

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Polygon:A frequency polygon is the geometric shape obtained by connecting with straight lines the midpoints of adjacent intervals of a histogram. Class marks will be shown on x-axis and frequency on y-axis.

Cumulative frequency Curve or Ogive:Ogive is a continuous cumulative frequency curve. An ogive is a graph that represents the cumulative frequencies for the classes in a frequency distribution. It shows how many of values of the data are below certain boundary.

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Statistical Quantities:

Arithmetic Mean:Arithmetic mean is mid value of the item in data. Mean is called as the central value of a distribution. Arithmetic mean is commonly referred to as "average" or simply as "mean". A mathematical representation of the typical value of a series of numbers, computed as the sum of all the numbers in the series divided by the count of all numbers in the series. The formula for the arithmetic mean is

• = Sum (fx/f)

Arithmetic Mean is the most easily understood and commonly used type of method. It is a good method of comparison of two series of data and can be calculated for almost every kind of data. But the major disadvantage is that Arithmetic mean is greatly affected by the extreme value and can not be calculated for qualitative data.

Median:Median is the value of the middle item of a series when it is arranged in ascending or descending order of magnitude. Median divides the series in two equal parts. Median is located in such away that in one part the items are less than or equal to median and in other part the items are more than or equal to median.Median is also easily calculated and easily understandable. The major advantage of median is that it can be located even when the data is incomplete but the total no. of observation is known. And the main disadvantage is that it varies from sample to sample.

Mode:The word mode is derived from the French word “LAMODE” mean fashion. Mode is the most frequent value in a data set. In other words the maximum point of the frequency distribution is called mode.It is the positional average based on position of item within series. The other advantage is that it is useful for non-quantitative data also. The major disadvantage of mode is that it can not be defined rigidly by mathematical formula (not based on principles of mathematics).

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Frequency Distribution from a Raw Data:

Six (6) Years Sales and Profits of Saydon Pharma:

Half Year (6 months) Saydon Sales (In Million Rupees)

Profit (In Million Rupees)

Profit percentage

1 Jan - 30 Jan 2003 60 12 20

1 July - 31 Dec 2003 62 12.4 20

1 Jan - 30 June 2004 72 18 25

1 July - 31 Dec 2004 65 16.25 25

1 Jan - 30 June 2005 76 19 25

1 July - 31 Dec 2005 77 19.25 25

1 Jan - 30 June 2006 76 22.8 30

1 July - 31 Dec 2006 80 24 30

1 Jan - 30 June 2007 93 18.6 20

1 July - 31 Dec 2007 97 19.4 20

1 Jan - 30 June 2008 93 18.6 20

1 July - 31 Dec 2008 95 19 20

• The following frequency distribution calculation and techniques are based on the sales and profits of Saydon Pharma from year 2003 to 2008.

Frequency Distribution Technique for Sales of Saydon Pharma:

Raw Data: 60, 62, 72, 65, 76, 77, 76, 80, 93, 97, 93, 95Sales in Arranged form: 60, 62, 65, 72, 76, 76, 77, 80, 93, 93, 95, 97Range: 97 – 60 = 27Class Interval: 54 – 65, 66 – 77, 78 – 89, 90 – 101Class Interval Size: 12Class Midpoint: 5.5

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No. of Sales in Million Frequency Cumulative Boundaries

54 – 65 3 53.5 – 65.5

66 – 77 4 65.5 – 77.5

78 – 89 1 77.5 – 89.5

90 – 101 4 89.5 – 101.5

Frequency Distribution Technique for Profits of Saydon Pharma:

Raw Data: 12,12.4, 18, 16.25, 19, 19.25, 22.8, 24, 18.6, 19.4, 18.6, 19Profits in Arranged form: 12, 12.4, 16, 16.25, 18, 18.6, 18.6, 19, 19.25, 19.4, 22.8, 24Range: 24 – 12 = 12Class Interval: 10 – 15, 16 – 20, 21 – 25Class Interval Size: 6Class Midpoint: 2.5

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No. of Profits in Million Frequency Cumulative Boundaries

10 – 15 2 9.5 – 15.5

16 – 20 8 15.5 – 20.5

21 – 25 2 20.5 – 25.5

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Mean, Median & Mode of Number of Sales of Saydon Pharma over Last Six Years:

No. of Sales in Million

Frequency (f) Cumulative Boundaries

Mid-Point FX = F*MP

53 – 65 3 52.5 – 65.5 59 177

66 – 78 4 65.5 – 78.5 72 308

79 – 91 1 78.5 – 91.5 85 85

92 – 104 4 91.5 – 104.5 98 392

Total 12 962

• Mean:• = Sum (fx/f)• = 962/ 12• = 80.16

This shows that on average over last six years Saydon Pharma made Rupees 80.16 million sales per Year.

• Median:


Frequency (f) Cumulative Boundaries

Cumulative Frequency

53 – 65 3 52.5 – 65.5 3

66 – 78 4 65.5 – 78.5 7

79 – 91 1 78.5 – 91.5 8

92 – 104 4 91.5 – 104.5 12

Total 12

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To calculate median, first median class will be obtained with the help of formula i-em = The size of (n/ 2)th item.Here n = sum of frequency

m = The size of (12/ 2)th itemm = the size of 6th itemAs 6 fall in cumulative frequency of 7 having class boundary of 65.5 – 78.5, So median class = m = 65.5 – 78.5. Now we will find which value is median in this median class by the following formula i-eM = l1 + h/f (m-c)Asl1 = Lower class limit = 65.5l2 = Upper class limit = 78.5h = Height (l2 – l1) = 13f = Frequency of median class = 4m = Median value of the class = 6c = Cummulative frequency of preceding median class = 3

Now putting values in the formula M = l1 + h/f (m-c) we get:M = 65.5 + 13/4 (6-3)M = 65.5 + 13/4 (3)M = 65.5 + 3.25 (3)M = 65.5 + 9.75Median = 80

• Mode:To find mode, first calculate model class.

How to calculate model class?F1 = Original frequencies of values & should be in the first column.F2 = Pairing of frequencies from top to bottom.F3 = Leaving the first value and pairing the rest of values.F4 = Making triplets.F5 = Leaving the first value and then making the triplets.F6 = Leaving the first two values and then making the triplets.

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Cumulative Boundaries

Frequency (f1)

Frequency (f2)

Frequency (f3)

Frequency (f4)

Frequency (f5)

Frequency (f6)

53 – 65 52.5 – 65.5 3 7

66 – 78 65.5 – 78.5 4 5

8_

79 – 91 78.5 – 91.5 1 5

9

92 – 104 91.5 – 104.5 4

Analysis Table:

Columns Classes having highest frequency Repetition

1 65.5 – 78.5, 91.5 – 104.5 52.5 – 65.5 (2 times)

2 52.5 – 65.5, 65.5 – 78.5 65.5 – 78.5 (5 times)

3 65.5 – 78.5, 78.5 – 91.5 78.5 – 91.5 (3 times)

4 52.5 – 65.5, 65.5 – 78.5, 78.5 – 91.5 91.5 – 104.5 (2 times)

5 65.5 – 78.5, 78.5 – 91.5, 91.5 – 104.5

6 ___

So model class = 65.5 – 78.5 (most frequent)

Now we will find mode from model class.Mode = {l1 + fm – f1 / 2(fm) - f1 – f2} * hAsl1 = Lower class limit of model class = 65.5l2 = Upper class limit of model class = 78.5h = Height (l2 – l1) = 13fm = Frequency of model class = 4f1= Frequency of the class preceding to model class = 3

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f2 = Frequency of class proceding to model class = 1Now putting the values in formula l1 + {fm – f1 / 2(fm) - f1 – f2} * hMode = 65.5 + {4 – 3 / 2(4) - 3 – 1} * 13Mode = 65.5 + {1 / 8 - 4} * 13Mode = 66.5 + {1 / 4} * 13Mode = 66.5 + {0.25 * 13}Mode = 66.5 + 3.25Mode = 68.75

Analysis of the Statistical Quantities:Good average is the one which is rigidly or well defined and not effected by abnormal large or small values or extreme values. Among all the three methods which is discussed and solved for sales of Saydon Pharma, The Arithematic mean i.e. mean method is more appropriate to estimate the average sales of Saydon Pharma over last six years, as all the values are in the range and no abnormality in the values. Therefore it can determined with the accuracy and represent the whole data set. The mean value shows that on average over last six years Saydon Pharma made 80.16 million Rupees sales per Year.Similarly median is also near to the mean value which is 80 million rupees sales per year, which also shows the accuracy. But the main disadvantage of the median is that it can not be detected exactly in the case of continuous series of observation. Whereas mode which gives the result of 68.75 million rupees sales per year, which is a different answer from the other results (mean and median) and the figures are little bit far away. But we cant say the mode answer accurate, as it ignores a high proportion of data and only represents the most frequent and common data and excluding every other value in the data. Therefore it can be unrepresentative and un-reliable.

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Forecasting:Prediction of future conditions is called forecast. The businesses must plan for the future. Planning for the future involves forecasting. Forecasting is an Integral Part of Business Planning. Businesses are very much keen about their future; they want to know what will happen to them and to their company’s status. Anything if it is going wrong then the companies plan accordingly to reduce the uncertainty. The objective of business forecasting is to minimize risk and the margin of uncertainty in business.Forecasting could be based on the followings:

1) Future Sales2) Total Market and Market Segmentation3) Company Forecast and Industry Forecast4) Short Term and Long Term Forecasting

Various formalized method of forecasting:Statistical forecasting is little bit different from other forecasting because past as an experience guide line is used to predict the future by identifying trends and patterns to develop a forecast. There are two approaches through which forecasting can be done.• Qualitative Method• Quantitative Method

Qualitative Method:The first method is qualitative method which is mostly used for short-term forecasting. In this method we obtain information about the intentions of the spenders through collecting experts’ opinion or by conducting interviews with the consumers.Quantitative Method:The second method is quantitative and is used for long-term forecasting. In this method, past experience is used as a guide line to predict the future by identifying trends and patterns to develop a forecast or future demand.

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Quantitative Methods (Statistical Methods):1. Regression Analysis:Regression is basically the dependence of one variable on the other variable. It is the statistical procedure which helps in predicting or estimating an unknown value of variable (dependent) from the known value of another variable (independent).

a) Multiple Regression Analysis: This method is used only when there are two or more than two variables. The main purpose of this method is to assess which factors to include and which to exclude.

b) Non-Linear Regression: This method is used when time becomes independent variable.

2. Time Series Analysis:Chronological arrangement of data or arrangement of values according to time is called time series analysis. The analysis of the time series identifies patterns, once the patterns are identified, they can be used to develop a forecast. A particular Time Series has four features called components i.e. linear trend (L), Seasonal Variations (S), Cyclical Variations (C), and Random or Irregular variations (R).

• Linear Trend refers to the long run increase or decrease in the series.• Seasonal Variation refers to the variations caused by weather patterns social habits such as

festivals etc.• Cyclical Variation refers to the rhythmic variations in the economic series.• Random Variation refers to the irregular and unpredictable shocks to the system, such as wars,

strikes etc.

3. Moving Averages: Moving average is one of least square method. Moving averages simply measure the average price or exchange rate of a currency pair over a specific time period. The Moving Average for ‘n’ months is found by simply summing up the demand during the past ‘n’ months and then dividing this total by ‘n’.

Moving Average = Demand in the previous ‘n’ months

n

4. Method of Least Square:This method is commonly used for fitting a straight line trend. This trend is called the line of the best fit, and the method is known as the method of least squares because the sum of squares of the differences which each of the points on the graph bear to the trend is least.

5. Exponential Smoothing: In this technique, more weightage or preference is given to the recent data. This is based on the argument that the more recent the observations, the more its impact on future.

6. Inspection Method:Inspection method is kind of observation because in this method the line of best fit is drawn by eye. The line is drawing in such a way that it appears to lie evenly between the recorded points.

(Statistical Forecasting, Date Accessed 10/05/2009)

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Comparison on Different Formalized Method of Forecasting:The following is the comparison of different methods applied to the sales and profits of Saydon Pharma for a period of six years and the forecast of their future sales & profit whether it will be increasing or decreasing.

Chart Showing Sales and profits of Saydon Pharma for Six Years Period:Half Year (6 months) Saydon Sales

(In Million Rs)Roryan Sales (In Million Rs)

Total Sales of Saydon after merging with

Roryan Pharma (In

Million)

Total Profit of Saydon

Pharma (In Million Rs)

Total Profit percentage of

Saydon Pharma

1 Jan - 30 June 2003 60 - 60 12 20

1 July - 31 Dec 2003 62 - 62 12.4 20

1 Jan - 30 June 2004 72 - 72 18 25

1 July - 31 Dec 2004 65 - 65 16.25 25

1 Jan - 30 June 2005 76 - 76 19 25

1 July - 31 Dec 2005 77 - 77 19.25 25

1 Jan - 30 June 2006 76 - 76 22.8 30

1 July - 31 Dec 2006 80 - 80 24 30

1 Jan - 30 June 2007 70 23 93 18.6 201 July - 31 Dec 2007 72 25 97 19.4 201 Jan - 30 June 2008 70 23 93 18.6 201 July - 31 Dec 2008 70 25 95 19 20

Here we changed two intervals of 6 months into complete 1 year by addition method for showing sales and profits on annual bases.

Interval Year Total Sales of Saydon Pharma (In

Milli0n R.s)

Total Profit of Saydon Pharma (In

Million Rupees)

1 Jan - 31 Dec 2003 1 122 24.4

1 Jan - 31 Dec 2004 2 137 34.25

1 Jan - 31 Dec 2005 3 153 38.25

1 Jan - 31 Dec 2006 4 156 46.8

1 Jan - 31 Dec 2007 5 190 38

1 Jan - 31 Dec 2008 6 188 37.6

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Correlation Coefficient (r):Relationship existing between two variables in such a way that a movement in the values of one variable find the response with the movement in the values of another variable, either in the same direction or in opposite direction. It is the most widely used method which assumes linear relationship. The coefficient of correlation, r explains the relative importance of the relationship between x and y. The absolute value of r shows the strength of the relationship. r can take on any value between –1 and +1.Here is the correlation between two variables i.e. sales and profit of a Saydon Pharma.

Interval Total Sales of Saydon Pharma (In Million Rs)

x

Total Profit of Saydon Pharma (In Million Rs)

y

xy X2 Y2

1 Jan - 31 Dec 2003 122 24.4 2976.8 14884 595.36

1 Jan - 31 Dec 2004 137 34.25 4692.25 18769 1173.06

1 Jan - 31 Dec 2005 153 38.25 5852.25 23409 1463.06

1 Jan - 31 Dec 2006 156 46.8 7300.8 24336 2190.24

1 Jan - 31 Dec 2007 190 38 7220 36100 1444

1 Jan - 31 Dec 2008 188 37.6 7068.8 35344 1413.76

Total 946 219.3 35110.9 152842 8279.48

The mathematical formula for computing r is:

r = 6( 35110.9 ) – 946(219.3) .

2 2

r = 210665.4 – 207457.8

r = 3207.6 = 3207.6 144(28.006) 4032.8

r = 0.795Note: If r2 = 0.624, then it becomes coefficient of determination which shows that 62% variation is one variable and 38% is another variable.

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Regression Method:The least square method of linear regression analysis provides a technique for estimating the equation of a line of best fit. It establishes a relationship between a dependent variable and one or more independent variables. In this method we assume that whether the trend line is upward or downward with a straight line. The equation for the least square regression line is y = a + bxX = Time (Independent Variable)Y = Sales of Saydon Pharma (Dependent Variable)a = Intercept of the line on the vertical axisb = Gradient of the line.

Now X = ∑x n

X = 946 = 157.66 6X = 157.66

Now Y = ∑y n

Y = 219.3 = 36.556

Y = 36.55

Now

b = 6(35110.9) – 946 (219.3) 6(152842) – (946)2

b = 210665.4 – 207457.8 = 3207.6 = 0.14 917052 – 894916 22136

b = 0.14

Now a = Y – bXa = 36.55 – 0.14(157.66)a = 36.55 – 22.07a = 14.48

Putting values in y = a + bx The fitted least square regression line for our equation is y = 14.48 + 0.14x

y = 14.48 + 0.14x, it can be represented graphically as well, which shows increase in the sales of Saydon Pharma in the future.

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Inspection Method:Inspection method is kind of observation because the line of best fit is drawn with the help of eyes. The line is drawn in such a way that it appears to lie evenly between the recorded points.

Note: There is an increasing or upward trend in sales of Saydon Pharma while decreasing or downwards trend in the profits.

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Extrapolation Method:In this method future predictions are based on the past results. This method can be applied only when actual results are plotted on a time series graph then this line can be extended or may say extrapolated into future according to the trend of past data.

Moving Averages:This method is related to calculating an average of several time periods. These are the consecutive averages of the results of a fixed number of periods.

Years Total Sales of Saydon Pharma (In Milli0n R.s)

Total Profit of Saydon Pharma (In

Million Rupees)

2003 122 24.4

2004 137 34.25

2005 153 38.25

2006 156 46.8

2007 190 38

2008 188 37.6

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Years Total Sales of Saydon Pharma (In Million Rupees)

3 years Moving Total of Sales

3 years Moving Averages of Sales

2003 122 – –

2004 137 412 137.33

2005 153 446 148.66

2006 156 499 166.33

2007 190 534 178

2008 188 – –

Note: The trend line shows an increasing trend in the sales of Saydon Pharma which is 178 minus 137.33 = 44.67%. Therefore the average trend has increased over three years because time is assumed at mid.

Average Increase: 44.67 = 14.89% 3

So forecasted value for year 2008 = Year 2007 value + Average increaseForecasted value for year 2008 = 178 + 14.89Forecasted value for year 2008 = 192.89

Similarly we can forecast for 2009 and 2010 also.E.g. 2007 = 1782008 = 178 + 1(14.89) = 192.892009 = 178 + 2(14.89) = 207.782010 = 178 + 3(14.89) = 222.67

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Analysis (Choosing the Right Forecasting Methodology):We studied above different formalized methods of forecasting and their comparison. Now we have to select the appropriate method of forecasting for our data.

The method of extrapolation and inspection assumes that the pattern of the increase in the sales of Saydon Pharma is stable and will remain the same in future, while on the other hand their profit showed decrease. This forecasting might be true only for short term purposes. Making of long term forecasting based on these methods will be very un-reliable and does not hold true because the unforeseen conditions and the un-stability in the economic conditions can challenge the reliability of this method.

A regression analysis usually begins by asking how to describe (by a straight line) the relationship between the explanatory variables and the dependent variable. The increasing trend shown by the best fitted line of sales in case of Saydon Pharma is not reliable because this trend is not true and not showing the actual profits obtained by these sales. In reality the increase in sales was due to merging of Saydon Pharma with Roryan Pharma. It does not show the cost involved in getting such results. When costs on these sales were brought into consideration there was immediate fall in the graph of real profit of Saydon Pharma. So the best fitted line drawn in regression analysis is not always reliable, it varies from case to case.

According to our data and comparison with the different methods, a method of moving averages seems to be the most appropriate for our data. This method seems to be more accurate for short term forecast in a stable economic condition. But there are also some disadvantages of moving averages, forecasting further into future become less accurate because projection are made entirely on past data. All forecast are subject to error which varies from case to case. The more and more forecasting of the future, the more unreliable the forecast is. Beside these factors, pattern of trend variations cannot be guaranteed to continue in the future because there are so many unforeseen factors involved. Moreover if the data available is limited then the future forecast becomes very unreliable, but in our case the data is sufficient for short term forecast of two years. So among all the mentioned and calculated forecasting methods, a method of moving averages seems to be more accurate and appropriate for our case.

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Reliability of Forecasts:The term reliability means "repeatability" or "consistency". A statistical forecast is considered reliable if it would provide repeatable consistent results with minimum or no error.

1. Data availability: Forecasting is made on the basis of the availability of primary or secondary data and therefore the required data should be collected initially for making forecast.

2. Simplicity: Depending upon the objectives, the forecaster should apply a simple and straight forward method of forecasting.

3. Skill: The relative accuracy of the forecast depends on the skills of the forecaster. The more experienced the forecaster is then the more accurate will be their forecast.

4. Resolution: The forecast system has resolution, if it can successfully sort out the set of events into subsets with different frequency distribution and separate one type of outcome from another.

5. Accuracy: Accuracy is how well the forecasted values match the actual values. Data may always not be reliable or accurate, so the forecaster must use more than one method to check the accuracy of the forecast. An appropriate choice of method ensures more accurate results and lowers the chances of errors.

6. Reliability: A time tested method increases the reliability of that method. If a particular method used to give reliable result in the past then the same method can be used for forecasting in future.

7. Durability: The forecast that are made should be valid in the long term because there is a lap of time in predicting the forecasts and the period when the product is likely to enter the market.

8. Economical: Although there may be different methods of making forecast and use of more than one method will definitely produce reliable result but it may be very expensive. It is therefore recommended that only one method which is more reliable and economical should be adopted for forecasting.

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Assessment of the Reliability of the Forecasted Result:The reliability of assessment of our results is based on the following points.

1. Data availability: Forecasting is made on the basis of the availability of primary or secondary data. In our case data was easily obtained from both primary and secondary sources. We faced no difficulty in collection of our data. This was the first step towards the reliability of our forecast.

2. Simplicity: The simplicity of data provides easy approach and grasping of the problem. In our case our approach was very simple and straight forward. We took two variables i.e. sales and profits of Saydon Pharma for a fix and short interval of time.

3. Skill: Skill is one of the important factors for apprehending and handling of problem. The relative accuracy of the forecast depends on the skills of the forecaster. The more experienced the forecaster is then the more accurate will be their forecast. Though we were not having much experience but in the use of inspection and extrapolation method, we keenly observed and obtained the required results.

4. Accuracy: The forecaster must use more than one method to check the accuracy of the forecast. Accuracy is how well the forecasted values match the actual values. An appropriate choice of method ensures more accurate results and lowers the chances of errors. We checked different methods of forecasting for our problem but we ultimately selected the method of moving averages to forecast our result. As this method is a time tested method which increases the reliability of our result.

5. Durability: The durability of forecast depends on its accuracy for a long term period because there is always laps of times in prediction and achievement of results. This durability can easily be seen in our analysis, as we based our results on the past six year period and predicted for the coming two years.

Justification of our Forecasted Result:As mentioned above, all the five points which are required for accuracy and reliability of forecasted result are applicable in our case. We always took care of these basic requirements in obtaining and analyzing our data. Different methods of forecasting were applied. But ultimately the time tested method of moving averages of forecast was used to analyze our data.

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Conclusion

Planning for the future involves forecasting. No business organization can ignore forecasting if they want to thrive and prosper in business. The objective of business forecasting is to minimize risk.

In the given scenario, one of the prospering organizations Saydon Pharma took a step of mergence without consultation with experts but they failed to obtain the required objectives. When they realized that they were in hot waters, they took consultancy from consultant where we were working as internee. The task was given to us. We studied their problem thoroughly and analyzed diligently. Proper survey was carried out, data was collected from various sources and statistical techniques were applied for our forecasting. Apparently there was increasing trend in the sales of Saydon Pharma after mergence with Roryan Pharma but the profit ratio was showing decline due to the reason that the incurring cost on the production which were not foreseen and estimated before mergence put them under stress due to extra expenses and thus the required profit could not be obtained with immediate effect. Their profit may increase with the passage of time for which they have to wait for a long period. But it is not possible in the near future. It is therefore recommended that the Saydon Pharma should quit this mergence immediately to reduce their losses and should concentrate on their old Pharmaceutical Company i.e. Saydon Pharma.

Hence it is recommended for every organization to plan for future by getting consultation and forecast from experts to avoid losses and minimize their risks.

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REFERENCE LIST

Book:

• BTEC. (2001) HNC HND Business, Core unit 5: Quantitative Techniques for Business: BPP Publishing.

Web:

Statistical Forecasting, Date Accessed 10/05/2009http://www.statisticalforecasting.com/forecasting-regression-analysis.php

Forecasting, Date Accessed 10/06/2009

http://www.bom.gov.au/bmrc/wefor/staff/eee/verif/verif_web_page.html

Sampling Methods, Date Accessed 05/06/2009www.encyclopedia.com/doc/1O13-samplingmethods.html

Persons:

• Sayed Muhammad Tariq, Chief Executive of Saydon Pharmaceutical Company.

• Sayed Abdul Rehman, Managing Director of Saydon Pharmaceutical Company.

• Mr. Nadeem Hassan, National Sales Manager of Saydon Pharma Company.

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AGENDA

Course Title: HND BusinessUnit Number and Title: Quantitative Techniques for BusinessAssessment Title: Use of statistical techniques to collect and analyze data, Production of forecasts based on formalized procedures and application of quantitative techniques to business situations.Outcome Number: 1, 2

Names of Group members:-Sayed Muhammad AliMuhammad Haris

Meeting No. 1:

Time: - 08:45 am to 11:30 amDate: - 27th may, 2009Venue: - Ali’s home, Shaheen Town.

Purpose of Meeting: In this meeting, we discussed the assignment brief in detail. We made a schedule for completing the assignment and selected the Saydon Pharmaceutical Company for our report.

Internal Verifier: Miss Sadaf Ijaz.

Lecturer: Sir Noor Muhammad

Signature: ______________________

38


AGENDA

Course Title: HND BusinessUnit Number and Title: Quantitative Techniques for BusinessAssessment Title: Use of statistical techniques to collect and analyze data, Production of forecasts based on formalized procedures and application of quantitative techniques to business situations.Outcome Number: 1, 2

Names of Group members:-Sayed Muhammad AliMuhammad Haris

Meeting No. 2:

Time: - 10:45 am to 11:30 amDate: - 1st June, 2009Venue: - Ali’s home, Shaheen Town.

Purpose of Meeting:

In this meeting we made a program for visit of the Saydon Pharmaceutical Company for collection of primary and secondary information for our report.

Internal Verifier: Miss Sadaf Ijaz.

Lecturer: Noor Muhammad

Signature: ______________________

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Documents

Quantitative Techniques of Business (QTB Report Saydon Pharma)