Question

if the median of data (arranged in ascending order) 31,33,35,x,x+10,48,48,50 is 40,then find value of x.

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Answer 1

Given,

The median of data (arranged in ascending order) 31,33,35,x,x+10,48,48,50 is 40.

To Find,

The value of x =?

Solution,

It is given that the median of the data arranged in ascending order is 40. We have to find the value of x.

$Data = 31,33,35,x,x+10,48,48,50$

$Median = 40$

The number of observations present in the data is even.

Therefore, the formula for finding the median for an even set of observations is given as:
$Median = \frac{(\frac{n}{2})^{th}\: term +( \frac{n}{2} + 1)^{th}\: term }{2}$

Where, $n = The\: number\: of\: observations$

Here, $n = 10$

Substituting the values in the above formula,

$40= \frac{(\frac{10}{2})^{th}\: term +( \frac{10}{2} + 1)^{th}\: term }{2}$

$40 = \frac{(5)^{th}\: term +( 5 + 1)^{th}\: term }{2}$

$40 = \frac{(5)^{th}\: term +( 6)^{th}\: term }{2}$

The 5th term is x and the 6th term is x + 10.

$40 = \frac{x + x + 10}{2}$

$40*2 = 2x + 10$

$80 - 10 = 2x$

$70 = 2x$

$x = \frac{70}{2} = 35$

Hence, the value of x is equal to 35.