Question

ii) If the observations 20, 22, 23, 25, (x + 1), (x + 3), 36, 38, 39 and 41 have median 30, then the value

of x is :​

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

The given set of observations are

• 20, 22, 23, 25, (x + 1), (x + 3), 36, 38, 39, 41

Here, number of observations are 10.

• This implies, n = 10 (which is even)

Median = 30

We know, median, when number of observations are even, is given by

$\bigstar \large\boxed{ \green{ \rm \: median \: = \dfrac{1}{2} {\bigg( {(\dfrac{n}{2} )}^{th} + {(\dfrac{n}{2} + 1)}^{th} \bigg)}}}$

On substituting, the values of median = 30 and n = 10

$\rm : \implies \:30 = \dfrac{1}{2} ( {5}^{th} observation \: + {6}^{th} observation)$

$\rm : \implies \:60 = x + 1 + x + 3$

$\rm : \implies \:60 = 2x + 4$

$\rm : \implies \:2x = 60 - 4$

$\rm : \implies \:2x = 56$

$\rm : \implies \:x \: = \: 28$

Answer 2

Answer:

Solution:−

The given set of observations are

20, 22, 23, 25, (x + 1), (x + 3), 36, 38, 39, 41

Here, number of observations are 10.

This implies, n = 10 (which is even)

Median = 30

We know, median, when number of observations are even, is given by

\bigstar \large\boxed{ \green{ \rm \: median \: = \dfrac{1}{2} {\bigg( {(\dfrac{n}{2} )}^{th} + {(\dfrac{n}{2} + 1)}^{th} \bigg)}}}