Question

Find the mean for each of the following frequency distribution

Class interval	Frequency
$0-20$ $20-40$ $40-60$ $60-80$ $80-100$ $100-120$ $120-140$	$12$ $18$ $15$ $5$ $26$ $15$ $9$

Answer 1

Step 1: Use the formula for mean of grouped frequency

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

Where,

$x_i$=Mid value of the class intervals.

$f_i$.=Values of frequency.

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	$x_i$	$f_i$	$f_i{x}_i$
$0-20$	$10$	$12$	$120$
$20-40$	$30$	$18$	$540$
$40-60$	$50$	$15$	$750$
$60-80$	$70$	$5$	$350$
$80-100$	$90$	$26$	$2340$
$100-120$	$110$	$15$	$1650$
$120-140$	$130$	$9$	$1170$
		$\sum f_i=100$	$\sum f_i{x}_i=6,920$

From the above table we get, $\sum f_i=100$ and $\sum f_i{x}_i=6,920$

Substituting the obtained values in the Arithmetic mean formula,

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

$=\frac{6,920}{100}=69.2$.

Final Answer:

Hence, the arithmetic mean value of the given frequency distribution is $=69.2$.