Page 167 - DMGT404 RESEARCH_METHODOLOGY

Unit 8: Descriptive Statistics

8.5 Keywords Notes

Average: It is a single value which can be taken as representative of the whole distribution.
Descriptive Statistics: Descriptive statistics are used to describe the basic features of the data in
a study.
Dispersion: It is the spread of the data in a distribution.
Median: It is that value of the variate which divides it into two equal parts.

Mode: It is that value of the variate which occurs maximum number of times in a distribution
and around which other items are densely distributed.

8.6 Review Questions

1. Show that if all observations of a series are added, subtracted, multiplied or divided by a
constant b, the mean is also added, subtracted, multiplied or divided by the same constant.

2. Prove that the algebraic sum of deviations of a given set of observations from their mean
is zero.
3. Prove that the sum of squared deviations is least when taken from the mean.
4. The heights of 15 students of a class were noted as shown below. Compute arithmetic
mean by using (i) Direct Method and (ii) Short-Cut Method.

S. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
No.
Ht. 160 167 174 168 166 171 162 182 186 175 178 167 177 162 163
(cms)

5. Compute arithmetic mean of the following series:

Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60
No. of Students 12 18 27 20 17 6

6. Calculate mode from the following data:

Mid-points 1 2 3 4 5 6 7 8

Frequency 5 50 45 30 20 10 15 5

7. Calculate median and mode from the following data:

Size 10 - 20 10 - 30 10 - 40 10 - 50 10 - 60 10 - 70 10 - 80 10 - 90
No. of 4 16 56 97 124 137 146 150
Students

8. Distinguish between an absolute measure and relative measure of dispersion. What are
the advantages of using the latter?

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