Question

Find the mean for each of the following frequency distribution

Class interval	Frequency
$10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$	$11$ $15$ $20$ $30$ $14$ $10$

Answer 1

Step 1: Use the formula for Arithmetic mean of grouped frequency data

Arithmetic Mean $=\frac{\sum f_i{x}_i}{\sum f_i}$

Where,

$x_i=$Mid value of the class intervals.

$f_i=$Values of the frequencies.

Step 2: Make the required frequency distribution table

First, we have to prepare the table values to find the values for $\sum f_i{x}_i$

Class interval	$x_i$	$f_i$	$f_i{x}_i$
$10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$	$15$ $25$ $35$ $45$ $55$ $65$	$11$ $15$ $20$ $30$ $14$ $10$	$165$ $375$ $700$ $1,350$ $770$ $650$
		$\sum f_i=100$	$\sum f_i{x}_i=4,010$

From the above table we get the values of,

$\sum f_i=100$

$\sum f_i{x}_i=4,010$

Substitute the obtained values in the formula,

Then, Arithmetic Mean $=\frac{\sum f_i{x}_i}{\sum f_i}$

$=\frac{4,010}{100}=40.1$

Final Answer:

Hence, the mean value of the given frequency distribution is $40.1$.