PROBABILITY and STATISTICS Math-102
Spring semester- 2011
Romasa [email protected]
P.S. Lecture slides are not substitute for the class lecture or course books.
STATISTICSWhat is Statistics?
Numerical FactsField or
Discipline of study
StatisticsThe consumer price index(CPI) fell by .3% in April (CNBC,
May 16, 2003)From the database of 3458 stock funds, only 172 funds
earned an A rating (Business week, January 27, 2003).At Marriott International, more than 40% of managers
worked their way up through the ranks (Fortune, January 20, 2003)
In Spring Semester, Math-102 class size in GIFT University is ------(GIFT News, march 8,2011).
Numerical facts in preceding statements (.3%, 172, 40%....) are called statistics.
STATISTICSApplication in Business and Economics
Accounting Finance Marketing Production Economics
STATISTICSStatistics is the art and science of collecting,
organizing, analyzing, presenting and interpreting data.
Assignment Q: Keeping in mind the above mentioned definition. Explain to your ‘Nanni Amma’, who faces difficulty in understanding technical terms and lengthy details, how you found out that, the number of female staff in GIFT university, Gujranwala has increased substantially over the past 4 years.
STATISTICSTypes of Statistics
Descriptive StatisticsIt consists of methods of organizing,
summarizing, and presenting data in an informative way.
Inferential StatisticsThe methods used to determine something
about the population on the basis of a sample.
STATISTICSCONCEPTS
DataData are those facts or figures that we collect, analyze and summarize for
presentation and interpretation.
Elements/memberElements are the entities on which data is collected.
VariableVariable is a characteristic of interest for the elements.
ObservationThe set of measurements obtained for a particular element is called an
observation.
PopulationThe set of all units of interest (finite or infinite). E.g. all students at GIFT
University, Gujranwala.
SampleA subset of the population actually observed. E.g. students in MATH- 102
class.
Types of DataData: A Set of measurementsQualitative DataQuantitative Data
ContinuousDiscreet
Based on the time they are collected, data can be classified as either cross-section, time series or panel data
Cross-section DataTime series DataPanel Data
Types of DataData: A Set of measurementsQualitative DataQualitative Data includes labels or names used to identify an
attribute of each element. E.g. Gender, Hair Color, Attitude towards war or capital punishment.
Quantitative DataQuantitative Data requires numeric values that indicate how
much or how many. A variable that can be measured numerically is called quantitative variable. Discrete, e.g. number of children, number of cars owned
by a familyContinuous. e.g. distance, temperature, time( between 30
and 40 mins), length, height
Types of DataData: A Set of measurementsCross-Sectional DataA cross-sectional data set consists of a sample of
individuals, households, firms, cities, states, countries, or a variety of other units, taken at a given point in time. E.g. the information on incomes of 100 families for 2005 is an example of cross-section data.
Time-series DataA time series data set consists of observations on a variable
or several variables over time. E.g. stock prices, money supply, consumer price index, gross domestic product, annual homicide rates, and cell phones sales figures.
Panel DataA panel data (or longitudinal data) set consists of a time
series for each cross-sectional member in the data set.
Cross section Data
Time Series Data
Panel Data
Levels of MeasurementData: A Set of measurementsThere’re four types of levels of measurement
1. Nominal level data2. Ordinal Level data3. Interval Level data4. Ratio level data
Levels of Measurement
Data: A Set of measurementsQualitative Data
Nominal, e.g. Binary (head, Tail), (Male, Female), hair color: black, golden, brown.
Ordinal, e.g. attitude to war or capital punishment: Strongly agree, Agree, Neutral, disagree, strongly disagree.
A qualitative variable is a variable with qualitative data.
Example on the Levels of MeasurementPizza Hut, Gujranwala asks their customers to rate the quality
of services.
How would you rate the quality of our services?Poor….Fair….Average……Good ….Excellent
orPizza Hut, Gujranwala asks respondents to rate the quality of
the service on a five-point scale (1-5) as:1 for poor2 for fair3 for average4 for good5 for excellent
We can reverse the coding method 1 for excellent and 5 for poor.
Levels of MeasurementData: A Set of measurementsQuantitative Data
Interval, e.g. Fahrenheit temperatureRatio (real zero), e.g. distance, number of
children
A quantitative variable is a variable with quantitative data.
Interval level DataQuantitative Data
Interval, e.g. Fahrenheit temperature
The third level of Data is interval data. One can say the temperature scales. E.g. 25 0C is warmer than 200C by exactly 50C. Also we can say that 250C is cooler than 300C by 50C.
But we cannot say that 300C is twice as warm as 150C because temperature measured in Celsius does not have an absolute zero point. That is the zero point is arbitrarily chosen and 00C shows some level of temperature. If we consider Fahrenheit in which 32 F corresponds to 00C and 68 F corresponds to 20 C and 500C corresponds 10 F then we cannot say that 200c is twice as warm as 100C
Interval level DataInterval Data provide not only greater than or
less than information, but also details on how much greater than or less than.
Interval data have no absolute zero point. So that we cannot use comparisons such as ‘twice as many’ or ‘half as much’ with interval data.
Ratio level DataHow many e-mail messages did you send
yesterday?How old are you?
The answer for both questions provides details about how much greater or less. They have an absolute zero point: 0 message means no message.
Sources of DataExisting Sources
Internal sources; such as companies own personnel files accounting records.
External sources; Organizations that specializes in collecting and maintaining data make available substantial amounts of business and economic data. E.g. Dow jones & company, Dun and Bradstreet, Bloomberg provide extensive business database to clients.
InternetGovernment Agencies
Statistical StudiesAt times data needed for a particular study is not available
through existing sources. Then usually statistical studies are conducted. They’re either experimental or observational.
Experimental studyHow a new drug affects blood pressure?
Observational/Non experimental studyStudies of smokers and non smokers are
observational studies as researchers do not attempt to control or determine who will smoke and who will not smoke.
Example 1
1. How many elements this data set contains?2. Which of the variable are quantitative and which are
qualitative?3. What is the average CD capacity for the sample?4. What percentage of the minisystem provides an FM
tuning rating of very good or excellent?5. What percentage of the minisystem includes two tape
decks?
Example 2State whether each of the following variable is
qualitative or quantitative and indicate its measurement scale.1. Age2. Gender3. Class Rank4. Make of Automobile5. Number of people favoring the death penalty6. Annual Sales7. Soft drink size ( small, medium, large)8. Employee Classification ( GS1 through GS18)9. Earning per share10. Method of payment( Cash, Check, Credit Card)
Example 3.What is your monthly pocket money?
0---10001500-25003000-45005000 & above
Example 3Regarding the monthly pocket moneyYou may think of an absolute zero point for
pocket money as no pocket money at allYou may think of comparisons, 1500 Rs is
twice as much as 3000 Rs.That leads you to deciding that pocket
monies are ratio data. But it is not Ratio Data
Example 3Reason
Respondents are asked to place themselves into one of the four categories of pocket money, so we can code these categories from 1 to 4 with 1 for the lowest and 4 for the highest amount.
If you are in the second category and Ayesha in the first we know that your income is higher than Ayesha, but we don’t know exactly how much higher, we cannot say as much as twice, therefore, in this case, we are collecting ‘Ordinal Data’.
ReferencesLind, A. Douglas, William G. Marchal and
Samuel A. Wathen, Basic Statistics for Business & Economics, 13th Edition, McGraw Hill/Irwin Publishing.
Mann, Prem S., Introductory Statistics, Sixth Edition 2005, John Wiley & Sons, Inc., Noida.
Anderson, Sweeney, Williams “Statistics for Business and Economics” 9th edition 2005 Thomson South-Western