Business Statistics I- BMS102

Business Foundation- 3rd semester

Assignment: Conceptual Questions, Problem solving and Case Analysis

Conceptual Questions [10]

1.  What purpose does measure of variation serve? In the light of this comment on some of the well-known measure of variations.

2.  What do you understand by ‘coefficient of variation’? Discuss its importance in business problems.

3.  Define moments. State the relationship between the moments about the mean (central moment) and moments about an arbitrary point (raw moment).

4.  What do you mean by ‘kurtosis’ in statistics? Give an example of use of kurtosis in business/finance.

5.  Measure of central tendency, dispersion, skewness and kurtosis are complementary to each other in describing frequency distribution. Elucidate.

Problem Solving [5]

1.  The share price of a company in Mumbai and Kolkota markets during the last ten months are recorded below

Month / Mumbai / Kolkota
January / 105 / 108
February / 120 / 117
March / 115 / 120
April / 118 / 130
May / 130 / 100
June / 127 / 125
July / 109 / 125
August / 110 / 120
September / 104 / 110
October / 112 / 135

Determine the standard deviations of prices of shares. In which market is the share price morestable?

2.  For the scores of 150 students in statistics given below, calculate the Karl Pearson’s coefficient of skewness and interpret it.

Marks(more than) / 0 / 10 / 20 / 30 / 40 / 50 / 60 / 70 / 80
No of students / 150 / 140 / 100 / 80 / 80 / 70 / 30 / 14 / 0

3.  Find the variance, skewness and kurtosis of the following frequency distribution by the method of moments:

Class Interval / 0-10 / 10-20 / 20-30 / 30-40
Frequency / 1 / 4 / 3 / 2

Comment on the nature of distribution

Case Analysis [5]

Here is a small set of data pertaining to grades for 30 students in Statistics 15 each from two sections. The range is from 1(failing) to 9(outstanding). The tutor is interested to see some of the descriptive statistics to find out which among the two sections has performed well and which section has more deviation. Due to the busy schedule of your tutor, he has provided the following information to you and asked you to calculate the given statistics. He has also ask you to give appropriate interpretation for the given distribution.

Section A Scores / 2 / 3 / 2 / 5 / 4.5 / 6 / 3.5 / 8 / 8.5 / 1 / 1.5 / 2.5 / 4.5 / 4.5 / 1.5
Section B Scores / 4 / 5 / 8 / 3.5 / 5.5 / 6.5 / 3.5 / 6 / 4.5 / 6 / 5.5 / 7 / 5 / 4 / 3

Give a comparative analysis of the score of two sections with following statistics

i.  Coefficient of variation

ii.  Karl Pearson’s co-efficient of skewness

iii.  Kurtosis (use the moment method)

Submission date: 21st Oct, 2016