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Business Data Analysis (BBA 104)

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Submitted By-Sangay Paldon

ID No.1807T3090014

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Table of Contents

1. Cumulative Frequency Curve ............................................................................ 2

1.1. Definition ..................................................................................................... 2

1.2. Usefulness of Cumulative frequency curve .................................................... 2

1.2. Example ....................................................................................................... 2

2. Frequency Table ................................................................................................. 4

2.1. Definition of frequency table .......................................................................... 4

2.2. General rule of constructing frequency table .................................................. 4

Discrete Frequency distribution table .................................................................... 4

Continuous frequency distribution table ................................................................ 6

3. Histogram ........................................................................................................... 8

3.1. Definition ........................................................................................................ 8

3.2. Features of Histogram ..................................................................................... 8

3.3. Example .......................................................................................................... 8

4. Frequency curve ................................................................................................. 9

4.1 Definition ......................................................................................................... 9

4.2. Features ........................................................................................................... 9

4.3. Example .......................................................................................................... 9

5. Bar chart ........................................................................................................... 10

5.1. Definition ...................................................................................................... 10

5.2. Simple bar charts........................................................................................... 10

5.3. Multiple bar charts ........................................................................................ 11

5.4. Component bar charts ................................................................................... 12

5.5. Percentage component bar charts .................................................................. 13

6. Pie chart ........................................................................................................... 14

6.1. Definition ...................................................................................................... 14

6.2. Features: ........................................................................................................ 14

6.3. Example: ....................................................................................................... 14

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1. Cumulative Frequency Curve

1.1. DefinitionCumulative frequency (Ogive) is a way to analyze the frequency distribution

table. It tells us how many data points are less than or within each of the class limits.

Cumulative frequency curve is hence the graphical representation of the

Ogive. The graph is drawn by plotting the value of first class on a graph then followed

by next plot which is the sum of first and second values, and so on.

1.2. Usefulness of Cumulative frequency curve

- To analyze what portion of data lies below or above certain level- To quickly find the upper and lower quartile, median, the range of the data and

percentile

- To show the distribution of data graphically and determine its skew- To clearly define the rate of change between classes.- To check the accuracy of calculation visually.- It has a widespread use in business and media- It is even used by marketers to evaluate the sales corresponding to the given

price range etc

1.2. ExampleYears Frequency Less than c.f More than c.f

0-5 5 5 34

5-10 8 13 29

10-15 3 16 21

15-20 10 26 18

20-25 6 32 8

25-30 2 34 2

Total frequency f 34

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Chart 12. Illustration:

The above curves represent the more than and less than cumulative frequencies.

The intersection between them is the median.

Median=

2

thitem

=34/2 th item=17

thitem

Median Class= 1520

Lower Quartile =

4

thitem

= 34/4th

item

= 8.5th

item

Lower quartile class= 510

Upper quartile =3

4

thitem

= 34

4

thitem

=25.5th

item

Upper quartile class= 1520

0

5

10

15

20

25

30

35

40

5 10 15 20 25 30

Less than c.f

More than c.f

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2. Frequency Table

2.1. Definition of frequency table

Frequency can be defined as the number of times a given data value is

repeated. For example if amount of Prada sold in a day is 100, then 100 is the

frequency of sales of Prada in a day.The table thus constructed by arranging the given data values with their

corresponding frequency in ascending/descending (generally ascending form

preferred) is called frequency table.

There are two types of frequency distribution table

a. Discrete frequency distribution tableb. Continuous frequency distribution table

Note: Individual frequency distribution does not need to be shown in tabular

form.

2.2. General rule of constructing frequency table

We use the following steps to construct a frequency table:

Step 1:

First we construct a table with three columns. The first column should contain all the

data values in ascending order of magnitude.

Step 2:

The second column should contain the tally bar. To make the tally bar, we first count

the number of times each data value repeats itself. We pull straight lines for each

count of data values. When four straight lines are pulled, the fifth count of data should

have a horizontal tally mark. Similarly, the process follows i.e. sixth, seventh, eighth,

ninth data count have straight tally marks while the tenth is a horizontal tally mark.

Step 3:

The number of tally marks is then counted and the value is put in the third column.

Discrete Frequency distribution tableData are presented with their corresponding frequency in this

distribution.

For example:The masses of people attending a survey are as below

50 51 55 50 52 51 50 56 54 51

51 55 53 55 50 53 56 52 54 53

50 55 52 56 50 52 54 51 52 56

The frequency table for discrete series can be presented as follows

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Mass ofSubject

Tally bar No ofpeople

50 |||| | 6

51 |||| 5

52 |||| 5

53 ||| 3

54 ||| 3

55 |||| 4

56 |||| 4

Total 30

Illustration:

The above example is constructed following the general rules of constructingfrequency table.

First of all, the given data value (masses) of people were recorded in ascending

order of magnitude. Here, 50 is the least value of mass so it goes first, then follows

the rest in ascending order. i.e.

Mass ofSubject


50

51

5253

54

55

56

Then, tally marks were made. Here, the first data is 50, so in the tally bar

column corresponding to 50 a tally mark was put. Similarly for 51, a tally mark was

put against 51 of tally bar column. The process continues and a table as shown below

is obtainedMass ofSubject


50 |||| |

51 ||||

52 ||||

53 |||

54 |||

55 ||||

56 ||||

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Finally, by counting the numbers of tally bar draw against the given data (mass

of subject), the third column was filled with the acquired number of counts. The final

figure is the same as shown in the example

Continuous frequency distribution table

Data are presented in a table by forming suitable class intervals

Example:Below are the ages of working no of population in a sample survey

18 19 20 19 21 23 2529 22 26 20 24 21 2022 28 30 35 32 39 3836 31 34 40 49 42 4550 47 46 41 40 52 5559 57 52 51 50 59 55

Sol:-

Here, Lowest Number (X min) = 18Largest Number (X max) = 59

Number of Items (n) = 42

Number of class = 1+ 3.322 log (n)= 1 + 3.322 log (42)

= 1+ 3.322 X 1.62

= 1 + 5.39

= 6.39 ~ 6

Range = X max - X min

= 5918

= 41

Class size = Range / No of class= 41/ 6.39

= 6.42 ~ 7

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Age group Tally bar Workingpopn

18-25 ||||| ||||| || 12

25-32 ||||| | 6

32-39 ||||| 5

39-46 ||||| | 6

46-53 ||||| ||| 8

53-60 ||||| 5

Total 42

Illustration:The above example was also constructed following the general rules for

constructing a frequency table.

Since the given data set is ranging from 18 to 60, it was better to use classintervals as the data range is wide. Using the above formulas, we find the class

interval and the number of classes.

Three columns were then drawn. The first column contains the data group with

class size of 7 each. The lower limit is 18 and the upper limit forms by adding 7 to it

i.e. 18+7=25, similarly the process follows and we obtain the following table


18-25

25-32

32-39

39-46

46-53

53-60

Then we draw a tally bar for every value of data against their given class interval.

Note: While striking a tally bar, the upper limit of a class interval is not included in

that group.


18-25 ||||| ||||| ||

25-32 ||||| |

32-39 |||||

39-46 ||||| |

46-53 ||||| |||

53-60 |||||

By counting the number of tally marks, we write down the numerical value in thethird column. The complete table is obtained as shown in the example

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3. Histogram

3.1. Definition

The term Histogram was introduced by Karl Pearson. Histograms are

basically, diagrams that use rectangles to represent frequencies. The area of each

rectangle is proportionate to the frequency it represents.

3.2. Features of Histogram

- Frequency of each data is represented by a rectangle that risesvertically from the horizontal axis.

- There are no gaps between the data in histogram, it is an absolute chart- The width of the rectangles can alter depending upon the class size of

the given data

- Histograms can only be produced if the frequency distribution iscontinuous

- Histograms can only be constructed if the frequency distribution hasclosed end class- Areas of rectangles are equal to the frequency of corresponding

frequencies.

3.3. Example

The population of a city (in million) between specific age groups were as men-tioned below:

Age group 0-10 10-20 20-30 30-40 40-50 50-60 60-70

Population 1 3 5 7 6 4 2

Chart 2

0

1

2

3

4

5

6

7

8

Population

Population of different age group

10

20

30

40

50

60

70

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4. Frequency curve

4.1 Definition

Frequency curve can be obtained by joining the midpoints of rectangles in a

Histogram through free hand. Frequency curves do not have sharp edges like

frequency polygon, rather it is smooth. It helps us understand the rate of increase anddecrease in frequency.

4.2. Features

- They are smoother than frequency polygon though the area covered bythem is same.

- They are free hand curve drawn through the vertices of frequencypolygon.

- It can be used to estimate the mean and find the skew- It can show central tendency, dispersion and modality- The curve begins and ends at the base line, it is also an absolute chart- The total area under the curve is approximately equal to the area under

a histogram or frequency polygon.

4.3. Example

The distributions of personal income ($1000) among the respondents (in 1000)are mentioned below:

PersonalIncome

0-10 10-20 20-30 30-40 40-50

No ofrespondent

5 9 6 7 3

Chart 3

0

1

2

3

4

5

6

7

8

9

10

10 20 30 40 50

Respondent

Personal income Vs Respondent

Respondent

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5. Bar chart

5.1. Definition

Bar charts are the most commonly used method to present data set. Bar chartsconsist of a set of rectangles each of which represents a set of data where the height of

the rectangle represents the magnitude of variables.

Some of the common features of bar charts are:- It is a one dimensional diagram- All bars are constructed on the same base line- The width of all the bars are uniform and equidistant spacing is

provided

- The height of a bar is proportional to the magnitude of variables- It can be drawn horizontally or vertically- It has a key or index at the top for better understanding of the diagram

There are varieties of bar charts. Some are mentioned below

5.2. Simple bar charts

Features:- It consists of single type of data.- It can make comparative study of two or more items or values of a

single variable

Example:The Sales of different products are given below:

Product Sales

A 5000

B 1000

C 8000

D 3000

Chart 4

0

2000

4000

6000

8000

A B C D

Sales 5000 1000 8000 3000

Sales

Products sold

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5.3. Multiple bar charts

Features:- It consist of Multiple data- It represents two or more sets of inter-related variables- Different bars are distinguished by different colors or patterns

Example: The number of sales of group A and group B are given below:

Years Group A Group B

2002 550 430

2003 250 510

2004 650 300

2005 100 760

2006 350 650

2007 420 550

Chart 5

2002 2003 2004 2005 2006 2007

Group A 550 250 650 100 350 420

Group B 430 510 300 760 650 550

0

100

200

300

400

500

600

700

800

Sale

s

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5.4. Component bar charts

Features:- A single rectangular box can be broken down into component part- It does a comparative study of different components with one another

and the relationship between the component with the total

- A single bar cannot accommodate excessive amount of componentsimply because of the fact that clustered diagrams make it difficult to

understand

Example:The total sales in ($10, 00,000) of a company is the sum total of the individualsales of all the brands of product of the company. The following data wasproduced in a company

Year Total Sales Brand A Brand B Brand C2005 530 200 190 140

2006 650 120 325 205

2007 570 370 100 100

2008 890 297 296 297

2009 756 500 100 156

Chart 6

200120

370297

500

190 325

100296

100

140

205100

297156

0

100

200

300

400

500

600

700

800

900

1000

2005 2006 2007 2008 2009

Sales

Brand A Brand B Brand C

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5.5. Percentage component bar charts

Features:- It is constructed on percentage basis of component form- It expresses relative importance of various components to the total- The height for all the bar is same i.e. 100

ExampleTaking the same example

Year Total Sales Brand A Brand B Brand C

2005 530 200 37.7% 190 35.9% 140 26.4%

2006 650 120 18.5% 325 50% 205 31.5%

2007 570 370 65% 100 17.5% 100 17.5%

2008 890 297 33.4% 296 33.3% 297 33.3%

2009 756 500 66.1% 100 13.3% 156 20.6%

To find the percentage component bar chart, the given data were converted into

percentage by using the following formula

Percentage of component data = Component data/ total of all the component * 100%

Chart 7

200

120

370

297

500

190

325

100

296

100

140205

100

297

156

2005 2006 2007 2008 2009

SalesBrand A Brand B Brand C

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6. Pie chart

6.1. Definition

A circle diagram divided into different sectors by radial lines such that the area of

each sector represents a component of the total value is called pie diagram

6.2. Features:

- It shows the relation between the components with one another and thetotal

- The areas of each sector are compared, therefore it is a twodimensional diagram

- The values of components are changed into degree, the total of degreeis 360

- If two or more set of data are presented for comparative study, then theradius of circles are proportional to the square root of their magnitude

- Different colors and patterns are used to distinguish the componentsfrom one another- It has a key or index to explain the effects

6.3. Example:

The data presented below shows the basic amount given by a domestic airline toeach airhostess per month in the year 2008.

Year 2008 Angle(2008)Salary 10,000 42.35o

Transport 5,000 21.18o

Allowance 50,000 211.76o

Food andlodging

20,000 84.71o

Total 85,000

Chart 8

10,000 5,000

50,000

20,000

Sales

Salary

Transport

Allowance

Food & lodging

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References:

Website: histogram: Definition from Answers.com Available at:http://www.answers.com/topic/histogram [Accessed On: 12 June 2010]

Website: Topic:Frequency Polygons and Cumulative Frequencies (Ogives) SharedExperienceProject Available at:http://shex.org/wiki/Topic:Frequency_Polygons_and_Cumulative_Frequencies_(Ogives) [Accessed On: 12 June 2010]

Website: Ogive Curve and Cumulative Frequency Curve | TutorVista.comAvailable at: http://www.tutorvista.com/content/math/statistics-and-probability/statistics-graphical-representation/ogive.php [Accessed On: 10 June2010]

Website: Essay: Demonstrate the usefulness of drawing a cumulative frequency

curve. Available at:http://www.coursework.info/GCSE/Information___Communication_Technology/ICT_Systems_and_Application/Demonstrate_the_usefulness_of_drawing_a_L63626.html[Accessed On: 12 June 2010]

Website: JSTOR: The Annals of Mathematical Statistics, Vol. 6, No. 1 (Mar.,1935), pp. 1-10 Available at: http://www.jstor.org/pss/2957555[Accessed On: 15June 2010]

Website: Frequency and Frequency Tables Available at:http://www.mathsteacher.com.au/year8/ch17_stat/03_freq/freq.htm[AccessedOn: 17 June 2010]

Website: Histogram - Wikipedia, the free encyclopedia Available at:http://en.wikipedia.org/wiki/Histogram[Accessed On: 12 June 2010]

Website: preciousheart.net ( Data Analysis: Displaying DataGraphs)Texas StateAuditor's Office, Methodology Manual, rev. 5/95 Available at:http://www.preciousheart.net/chaplaincy/Auditor_Manual/11grphd.pdf[Accessed On: 15 June 2010]
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Sangay Paldon(1807T3090014)