Business MathematicsTotal Marks: 100 (60 Theory + 40 Internal)

Internal Marks BreakupAttendance & Class

Participation10

Test 20

Assignment 10

Statistics

Statistics

• Statistics is the science of dealing with numbers.

• It is used for Collection, Summarization, Presentation and Analysis of DATA

Application of Statistics

• Marketing : Market research, choosing appropriate marketing strategy, etc

• Finance: Forecasting, ascertaining risks, etc

• Operations: Inventory management, manufacturing and distribution of manufactured item, etc

• Human Resources: Staff evaluation, ratings, compensation structure, etc

Limitations of Statistics

• Only quantifiable data is captured• Sampling is used so result may not be

accurate• Statistics reveal the average behaviour• Statistics in not 100% accurate

Subdivisions within Statistics

• Descriptive Statistics : Summarising the given data, bringing out their important features

• Inferential Statistics : Use of quantitative techniques that enable us to make approximate generalisations

Population and Sample

• A population is a collection of all elements under statistical investigation about which we are trying to draw some conclusion

• Small representative portion of population is called as Sample

Types of Data

Data can be classified in various ways as follows

1.Primary and Secondary2.Qualitative and Quantitative3.Discrete and Continuous

Primary and Secondary

• Primary data is collected for some specific purpose or study

• Secondary data is the data derived through some media like reports, newspapers, hand books, magazines, etc.

Qualitative and Quantitative

• Qualitative data is expressed by a non numerical property– Ex: satisfaction of a customer , opinion about a

product

• Quantitative data is numerically expressed– Ex: weight, height, income, etc

Discrete and Continuous

• Variable is said to be discrete if it assumes only some specific values in a given range.– Ex: number of customers visiting an outlet

• Variable is said to be continuous when some sort of measurement is involved– Ex: height, weight,

Presentation of Data

The first step in statistical analysis is to presentdata in an easy way to be understood.

The two basic ways for data presentation are• Tabular form– List, Frequency distribution.

• Graphical form– Bar chart, pie chart, histogram, etc

List Tables

• A table consisting of two columns, the first giving an identification of the observational unit and the second giving the value of variable for that unit.

Example : number of patients in each hospital department are

Department Number of patients

Surgery 50

ENT 15

Ophthalmology 10

Frequency Distribution Tables

• Ex: Assume we have a group of 20 individuals whose blood groups were as follows : A, AB, AB, O, B, A, A, B, B, AB, O, AB, AB, A, B, B, B, A, O, A.

We want to present these data by table.

Type of data??

Frequency Distribution Tables

Blood Group Frequency

A 6

B 6

AB 5

O 3

Total 20

Frequency Distribution Table

Ex: The Following data are Blood Pressure measurements (mmHg) of 30 patients with hypertension. Present these data in frequency table

150, 155, 160, 154, 162, 170, 165, 155, 190, 186, 180, 178, 195, 200, 180,156, 173, 188, 173, 189, 190, 177, 186, 177, 174, 155, 164, 163, 172, 160

Type of data??

Frequency Distribution Table

Blood Pressure Frequency

150 – 160 6

160 – 170 6

170 – 180 8

180- 190 6

190 – 200 3

200 – 210 1

Total 30

Graphical Representation

• Simple • Easy to understand• Save a lot of words• Self explanatory

Bar Charts

• It is used for presenting discrete data• It represent the measured value by separated

rectangles of constant width and its lengths proportional to the frequency

• Type:• Simple • Multiple • Sub Divided

Simple Bar Charts

• Ex: The following data gives the distribution of 200 MBA students at a management institute according to their educational qualifications

Qualification Number of Students

B.E. 55

B.Com 70

BMS/BMM 40

Others 35

0

20

40

60

80

Subdivided Bar Chart

• A subdivided bar chart is a chart wherein each bar is divided into further components.

Qualification Number of

Students

Metro Large Medium

B.E. 55 25 10 20

B.Com 70 40 15 15

BMS/BMM 40 20 10 10

Others 35 10 15 10

Multiple Bar Chart

• Multiple bar chart: Each observation has more than one value represented, by a group of bars. Percentage of males and females in different countries, percentage of deaths from heart diseases in old and young age, etcName Nov Dec

Lakshmi Mittal 20 32

Mukesh Ambani 7 15

Anil Ambani 5.5 18.2

Azim Premji 11 17.1

010203040

Lakshmi Mittal

Mukesh Ambani

Anil Ambani

Azim Premji

Pie Chart

• Consist of a circle whose area represents the total frequency (100%) which is divided into segments.

• Each segment represents a proportional composition of the total frequency.

Pie Chart

• Angle at the centre is calculated by formula

Qualification Number of

Students

% Angle

B.E. 55 28 99

B.Com 70 35 126

BMS/BMM 40 20 72

Others 35 17 63

0360100

xangle

Histogram

• It is very similar to the bar chart with the difference that the rectangles or bars are adherent (without gaps).

• It is used for presenting class frequency table (continuous data).

• Each bar represents a class and its height represents the frequency (number of cases), its width represent the class interval.

Histogram

Class Frequency

2000 – 3000 2

3000 – 4000 5

4000 – 5000 6

5000 – 6000 4

6000 – 7000 3

Frequency Polygon

• The polygon formed by joining the midpoints of the rectangles of histogram is known as the frequency polygon

Line Graph

• It is a visual presentation of a set of data values joined by straight lines.

Ex: Following is the data of business per employee in some banks

Bank Business Per Employee2005 - 06

Business Per Employee2001 – 02

Andhra Bank 426.75 195.96

Indian Bank 295 156

Canara Bank 441.57 214.88

Dena Bank 364 221

Bank of India 381 218.74

Line Graph

Summary

• Basics of Statistics• Types of data

End of Session 1