The following observations have been arranged in ascending order. If the median of the data is 63, find the value of $x: 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95$

Given:

$29, 32, 48, 50, x, x + 2, 72, 78, 84, 95$

The median of the data is 63.

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)

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

Here,

$n = 10$ which is even

Therefore,

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

$63= \frac{2x+2}{2}$

$63=x+1$  

$x=63-1$

$x=62$

The value of $x$ is $62$.

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Updated on: 10-Oct-2022

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