The observation 56,58,63,x-5,x+1,75,81,85 have been arranged in ascending order. If the median of the data is 67 , find the value of x .

Given:

The observations $56,58,63,x-5,x+1,75,81,85$ have been arranged in ascending order.

The median of the data is 67.

To do:

We have to find the value of $x$.

Solution:

We know that,

Median $= \frac{1}{2}[\frac{n}{2}th\ term+(\frac{n}{2}+1)th\ term]$  (when $n$ is even)

Here,

$n = 8$ which is even

Therefore,

Median $= \frac{1}{2}[4th\ term + 5th\ term]$

$67= \frac{1}{2}(x-5+x+1)$

$67= \frac{2x-4}{2}$

$2x-4= 67(2)$  

$2x=138$

$x=\frac{138}{2}$

$x=69$

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Updated on: 10-Oct-2022

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