Question

convert the following series into a simple frequency distribution : Mid value :=5, 15, 25, 35, 45, 55. Frequency := 2, 8, 15, 12, 7, 6 ​

Answer 1

Given:

Given that,

Mid values : 5,15,25,35,45,55 and

Frequency : 2,8,15,12,7,6 ​

To find:

We need to convert the given series into a simple frequency distribution.

Solution:

Before solving the question, we should find the class interval.

We know that, the class interval is given by the formula,

$m-\frac{s}{2}$ - $m+\frac{s}{2}$

Where $m$ is the mid value or mid point of the class and $s$ is the class size.

For the mid point 5,

$m=5$

$s=15-5=10$

So, class interval for mid point 5 is

$m-\frac{s}{2}$ - $m+\frac{s}{2}$ $=$ $5-\frac{10}{2}$ - $5+\frac{10}{2}$ = 0 - 10

Similarly,

For mid point 15, interval is 10 - 20.

For mid point 25, interval is 20 - 30.

For mid point 35, interval is 30 - 40.

For mid point 45, interval is 40 - 50.

For mid point 55, interval is 50 - 60.

So, the frequency distribution table is

Class                Frequency

0 - 10                        2

10 - 20                       8

20 - 30                     15

30 - 40                       12

40 - 50                       7

50 - 60                       6