Question

If the mean of the no. 6,4,3,8,10,11,10,10,5 and 'a' is 7.2 and the median of number 11,10,b,8,6,10,a,4,3 and 10 is is 8.5 then the value of b is:
(A)8
(B)9
(C)10
(D)7​

Answer 1

The value of b is 9, so the correct answer is the option (B) 9.

Given:

The mean of the data 6, 4, 3, 8, 10, 11, 10, 10, 5, and 'a' is 7.2  

The median of 11, 10, b, 8, 6, 10, a, 4, 3, and 10 is 8.5

To find:

The value of b  

Solution:

Formula used:

Mean of the data = [ Sum of observations ]/ Number of observations

Median of data = [ (n/2)th term + { (n/2)+1}th term]/2  

[ When the number of observations is even ]

Given that mean of  6, 4, 3, 8, 10, 11, 10, 10, 5, and 'a' is 7.2  

By the given formula,

Mean of the data = [ 6 + 4+ 3+ 8+ 10+ 11+ 10+ 10+ 5 + a]/10

= [ 67 + a ]/10

From the given data, [ 67 + a ]/10 = 7.2

=> 67 + a = 72

=> a = 5

Then the given both data will be  

6, 4, 3, 8, 10, 11, 10, 10, 5 and 5

11, 10, b, 8, 6, 10, 5, 4, 3 and 10

Here Median of 11, 10, b, 8, 6, 10, 5, 4, 3, and 10 is 8.5

Arrange the given data in ascending order

=> 3, 4, 5, 6, b, 8, 10, 10, 10, 11  

[ here we took b < 8 because any other value at that place can't give the median as 8.5 ]  

By the given formula

Median = [ (10/2)th term + { (10/2)+1}th term]/2  

= [ 5th term +6th term]/2  

=  [ b + 8] /2

From the given data,

=> [ b + 8] /2 = 8.5

=> [ b + 8 ] = 17

=> b = 17 - 8

=> b = 9

Therefore,

The value of b is 9, so the correct answer is the option (B) 9.

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