Page 104 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 6: Measures of Central Tendency

Notes
Example: Find out the missing item (x) of the following frequency distribution whose
arithmetic mean is 11.37.
X : 5 7 x 11 13 16 20
f : 2 4 29 54 11 8 4

fX 5 2 7 4 29x 11 54 13 11 16 8 20 4
X
f 112

10 28 29x 594 143 128 80
11.37 or 11.37 × 112 = 983 + 29x
112
290.44
x = 10.015 = 10 (approximately)
29

Example: The arithmetic mean of 50 items of a series was calculated by a student as 20.
However, it was later discovered that an item 25 was misread as 35. Find the correct value of
mean.
Solution.
N = 50 and X = 20 SX = 50 × 20 = 1000
i
990
Thus SX = 1000 + 25 – 35 = 990 and = = 19.8
i (corrected) (corrected) 50
Alternatively, using property 7:
10
average change in magnitude 20 =20 - 0.2 = 19.8
new old 50

6.2.4 Merits and Demerits of Arithmetic Mean

Merits

Out of all averages arithmetic mean is the most popular average in statistics because of its merits
given below:
1. Arithmetic mean is rigidly defined by an algebraic formula.

2. Calculation of arithmetic mean requires simple knowledge of addition, multiplication
and division of numbers and hence, is easy to calculate. It is also simple to understand the
meaning of arithmetic mean, e.g., the value per item or per unit, etc.

3. Calculation of arithmetic mean is based on all the observations and hence, it can be
regarded as representative of the given data.
4. It is capable of being treated mathematically and hence, is widely used in statistical analysis.
5. Arithmetic mean can be computed even if the detailed distribution is not known but sum
of observations and number of observations are known.
6. It is least affected by the fluctuations of sampling.
7. It represents the centre of gravity of the distribution because it balances the magnitudes of
observations which are greater and less than it.
8. It provides a good basis for the comparison of two or more distributions.

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