Page 131 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes Geometric Mean: The geometric mean of a series of n positive observations is defined as the nth
root of their product.
Harmonic Mean: The harmonic mean of n observations, none of which is zero, is defined as the
reciprocal of the arithmetic mean of their reciprocals
Measure of Central Tendency: A measure of central tendency is a typical value around which
other figures congregate.
Measure of Central Value: Since an average is somewhere within the range of data it is sometimes
called a measure of central value.

Median: Median of distribution is that value of the variate which divides it into two equal parts.
Mode: Mode is that value of the variate which occurs maximum number of times in a distribution
and around which other items are densely distributed.

Partition Values: The values that divide a distribution into more than two equal parts are
commonly known as partition values or fractiles.
Percentiles: Percentiles divide a distribution into 100 equal parts and there are, in all, 99 percentiles
denoted as P , P , ...... P , ...... P , ...... P , ...... P respectively.
1 2 25 40 60 99
Quartiles: The values of a variable that divide a distribution into four equal parts are called
quartiles.
Weighted Arithmetic Mean: Weights are assigned to different items depending upon their
importance, i.e., more important items are assigned more weight.

Weighted Geometric Mean: Weighted geometric mean of observations is equal to the antilog of
weighted arithmetic mean of their logarithms.

6.8 Review Questions

1. What are the functions of an average? Discuss the relative merits and demerits of various
types of statistical averages.
2. Give the essential requisites of a measure of ‘Central Tendency’. Under what circumstances
would a geometric mean or a harmonic mean be more appropriate than arithmetic mean?
3. 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
4. Calculate arithmetic mean of the following data:

: 10 12 14 16 18 20
: 3 7 12 18 10 5
5. Find out the missing frequency in the following distribution with mean equal to 30.
Class : 0 -10 10 - 20 20 - 30 30 - 40 40 - 50
Frequency : 5 6 10 ? 13
6. A distribution consists of three components each with total frequency of 200, 250 and 300
and with means of 25, 10 and 15 respectively. Find out the mean of the combined distribution.
7. The mean of a certain number of items is 20. If an observation 25 is added to the data, the
mean becomes 21. Find the number of items in the original data.

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