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Home » The median of the observations 11, 12, 14, (x – 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24. Find the value of x and hence find the mean.
The median of the observations 11, 12, 14, (x – 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24. Find the value of x and hence find the mean.
CBSE | Class 10 | Exercise 1 | Maths | Measures of Central Tendency | ML Aggarwal
The median of the observations 11, 12, 14, (x – 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24. Find the value of x and hence find the mean.

Solution:

Observation are as follows :

11, 12, 14, (x-2), (x+4), (x+9), 32, 38, 47

n = 9

Here n is odd. So median = ((n+1)/2)th term

= (9+1)/2 )th term

= 5th term

= x+4

Given median = 24

x+4 = 24

x = 24 -4 = 20

Sum of observations = 11+12+14+(x-2)+(x+4)+(x+9)+32+38+47

= 165+3x

Substitute x = 20

Sum of observations = 165+3×20

= 165+60

= 225

Mean = Sum of observations /number of observations

= 225/9 = 25

Hence the value of x is 20 and mean is 25.

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