# CLASS-10MEASURES OF CENTRAL TENDENCY - ARITHMETIC MEAN

Arithmetic Mean

The average of numbers in arithmetic is known as the Arithmetic Mean of these numbers in statistics.

Mean of an Ungrouped Data –

The arithmetic Mean or simply the Mean of ‘e’ observations x₁, x₂, x₃,……………….., xₑ is given by the formulae –

(x₁ + x₂ + x₃ +………………..+ xₑ)             ∑xₑ

Mean  = -----------------------------  =  --------

e                               e

In above said equation or formulae, symbol is called sigma stands for the summation of the term. Total number of term is ‘e’.

There are some examples are given below for your better understanding –

Example.1) Calculate the mean of the following numbers 4, 8, 12, 15, 20, 24, 7, 6, 22

Ans.)  Sum of the given numbers = (4 + 8 + 12 + 15 + 19 + 24 + 7 + 6 + 22) = 118

Total number of given numbers = 9

117

Mean of the given numbers = ------- =  13

9

So, the required mean number is 13   (Ans.)

Example.2)  Calculate the mean of the following numbers 5.5, 7.25, 12.55, 23, 16.75, 21.20, 6.15

Ans.) Sum of the given numbers = (5.5 + 7.25 + 12.55 + 23 + 16.75 + 21.20 + 6.15) = 92.4

Total number of given numbers = 7

92.4

Mean of the given numbers = -------- =  13.14

7

So, the required mean number is 13.14       (Ans.)