Discrete Series Arithmetic Mean

When data is given along with their frequencies. Following is an example of discrete series −

Items	5	10	20	30	40	50	60	70
Frequency	2	5	1	3	12	0	5	7

For discrete series, the Arithmetic Mean can be calculated using the following formula.

Formula

$\bar{x} = \frac{f_1x_1 + f_2x_2 + f_3x_3........+ f_nx_n}{N}$

Alternatively, we can write same formula as follows −

$\bar{x} = \frac{\sum fx}{\sum f}$

Where −

Problem Statement −

Calculate Arithmetic Mean for the following discrete data −

Items	14	36	45	70
Frequency	2	5	1	3

Solution −

Based on the given data, we have −

Based on the above mentioned formula, Arithmetic Mean $\bar{x}$ will be −

$\bar{x} = \frac{463}{11} \\[7pt] \, = {42.09}$

The Arithmetic Mean of the given numbers is 42.09.

Print Page