Question

The median of the following observations arranged in ascending order is 15.
10, 12, 14, x - 3 ,x, X + 2,25, then find x

Answer 1

Data : 10,12,14,x-3,x,x+2,25

Median =15

No of observation (n) =7(odd)

Median =n+1/2 (for odd)

15=8/2 th term

15=4th term

15=x-3

x= 15+3

x=18

The observations are 10,12,14,15,18,20,25

Answer 2

Given,

A set of observations arranged in ascending order: 10, 12, 14, x - 3,x, x + 2,25

Median of the set of observations = 15

To find,

The value of x.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

If a set of n observations are arranged either in ascending or descending order such then n is an odd integer, then,

the median of the set of data = value of the {(n-1)/2}-th term

{Statement-1}

According to the question,

The given set of observations arranged in ascending order: 10, 12, 14, x - 3 ,x, x + 2,25 has 7 terms

=> the median of the set of observations = {(7+1)/2}th observation = value of the 4th observation

the median of the set of observations = {(7+1)/2}th observation = value of the 4th observation

{according to statement-1}

=> 15 = x-3

{according to the question}

=> x = 15+3

=> x = 18

Hence, the value of x is 18.