Numbers $50, 42, 35, 2x + 10, 2x - 8, 12, 11, 8$ are written in descending order and their median is 25, find $x$.

Given:

Numbers $50, 42, 35, 2x + 10, 2x - 8, 12, 11, 8$ are written in descending order and their median is 25.

To do:

We have to find $x$.

Solution:

We know that,

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

$=\frac{n+1}{2}th\ term$    (when $n$ is odd)

Here,

$n = 8$ which is even

Therefore,

Median $= \frac{1}{2}(2x+10+2x-8)$

$25= \frac{1}{2}(4x+2)$

$25= 2x+1$  

$2x=25-1$

$2x=24$

$x=\frac{24}{2}$

$x=12$

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Updated on: 10-Oct-2022

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