Question

If the mode of the data is 34.5, find the missing frequency 'f':

Class
0-15
15 - 30
30 – 45
45 - 60
60 – 75
Frequency
2
7
f
3
7​
please answer!

Answer 1

Given:

Frequency distribution table.

Mode = 34.5

To find:

The value of missing frequency 'f'.

Solution:

Formula for mode is

`Mode=l+(f_1-f_0)/(2f_1-f_0-f_2)* h`

where, l is lower limit of modal class,
`f_1` is frequency of modal class,
`f_0` is frequency of preceding class,
`f_2` is frequency of succeeding class, h is class size.

Mode is 34.5, so the modal class is 30-45. So,

`l=30,f_1=f,f_0=7, f_2=3,h=45-30=15`

Putting these values in the above formula, we get

`34.5=30+(f-7)/(2f-7-3)* 15`

`34.5-30=(f-7)/(2f-10)* 15`

`4.5=(f-7)/(2f-10)* 15`

Divide both sides by 15.

`(4.5)/(15)=(f-7)/(2f-10)`

`0.3=(f-7)/(2f-10)`

`0.3(2f-10)=f-7`

`0.6f-3=f-7`

Separating variable terms, we get

`0.6f-f=3-7`

`-0.4f=-4`

Divide both sides by -0.4.

`f=(-4)/(-0.4)`

`f=10`

Therefore, the value of f is 10.