Page 98 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 6: Measures of Central Tendency

Notes
Did u know? An average is a single value which can be taken as representative of the whole
distribution.

Self Assessment

Fill in the blanks:
1. ............................ of the data is a necessary function of any statistical analysis.
2. The huge mass of unwieldy data is summarized in the form of ..................and ....................

3. A ................................. or an average is very essential and an important summary measure
in any statistical analysis.
4. An ......................... is a single value which can be taken as representative of the whole
distribution.
5. A measure of central tendency is a typical value around which other figures.......................
6. Different sets of data can be compared by comparing their ............................

7. AM and GM comes under ..............................averages.

6.2 Arithmetic Mean

Before the discussion of arithmetic mean, we shall introduce certain notations. It will be assumed
that there are n observations whose values are denoted by X ,X , ..... X respectively. The sum of
1 2 n
these observations X + X + ..... + X will be denoted in abbreviated form as, where (called
1 2 n
sigma) denotes summation sign. The subscript of X, i.e., ‘i’ is a positive integer, which indicates
the serial number of the observation. Since there are n observations, variation in i will be from
1 to n. This is indicated by writing it below and above , as written earlier. When there is
no ambiguity in range of summation, this indication can be skipped and we may simply write
X + X + ..... + X = X .
1 2 n i
Arithmetic Mean is defined as the sum of observations divided by the number of observations.
It can be computed in two ways: (i) Simple arithmetic mean and (ii) weighted arithmetic mean.
In case of simple arithmetic mean, equal importance is given to all the observations while in
weighted arithmetic mean, the importance given to various observations is not same.

6.2.1 Calculation of Simple Arithmetic Mean

When Individual Observations are given

Let there be n observations X , X ..... X . Their arithmetic mean can be calculated either by direct
1 2 n
method or by short cut method. The arithmetic mean of these observations will be denoted by.
Direct Method
Under this method, X is obtained by dividing sum of observations by number of observations,
i.e.,
n
X
i
i 1
X
n

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