Question

The mode of the series is 36 find x
0-10 10-20 20-30 30-40 40-50 50-60 60-70 8,10,x,16,12,6,7

Answer 1

this is your answer (10)

Answer 2

Answer:

The value of x is 10.

Step-by-step explanation:

Given : The mode of the series is 36.

To find : The value of x?

Solution :

Class :          0-10     10-20      20-30     30-40     40-50    50-60   60-70

Frequency :  8             10           x              16             12          6           7

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,

Mode = 36

So, The modal class is 30-40

l=30 , h=10 , $f_1=16$ ,$f_0=x$, $f_2=12$  

Substituting the value in the mode formula,

$36=30+(\frac{16-x}{2(16)-x-12})\times 10$

$6=(\frac{16-x}{20-x})\times 10$

$6(20-x)=10(16-x)$

$120-6x+10x-160=0$

$4x=40$

$x=10$

Therefore, The value of x is 10.