Question

1.Find the missing frequency f, if the mode of the given data is 154.









Classes



120-130



130-140



140-150



150-160



160-170



170-180



Frequency



2



8



12



f



9



7



plzz give an answer fast....

Answer 1

The answer is given below:-

Answer 2

Answer:

The value of f=18.

Step-by-step explanation:

Given : Data,  

Class :         120-130    130-140   140-150   150-160   160-170    170-180

Frequency :    2                8              12              f              9              7

To find : The value of f?

Solution :  

Formula to find the mode is  

$M=l+(\frac{f_1-f_0}{2f_1-f_0-f_2})\times h$

Where, l is the lower limit of the modal class  

h is the size of the class interval,

$f_1$ is the frequency of the modal class

$f_0$ is the frequency of the class preceding the modal class,

$f_2$ is the frequency of the class succeeding the modal class.

From the given data,

In the class interval 20-30 has highest frequency.

So, The modal class is 20-30

l=150 , h=10 , $f_1=f$ ,$f_0=12$, $f_2=9$  , M=154

Substituting the value in the mode formula,

$154=150+(\frac{f-12}{2(f)-12-9})\times 10$

$154-150=(\frac{f-12}{2f-21})\times 10$

$4=\frac{10f-120}{2f-21}$

$8f-84=10f-120$

$2f=36$

$f=18$

Therefore, The value of f=18.