Question

The numbers 50, 42, 35, (2x +10), (2x-8), 12, 11,8 have been written in
a descending order. If their median is 25, find the value of x.​

Answer 1

Answer : 50,42,35,2x+10,2x-8,12,11,8 are written descending order

Here n=8 which is even

since no. of observation is 6 , Median is the average of the middle data

The middle data =2x+10,2x-8

Hence 25= 2x+10+2x+8/2

25=4x+2/2

50=4x+2

4x=48

Hence x=12

Answer 2

Given: (i)The terms 50, 42, 35, (2x +10), (2x-8), 12, 11,8 are in descending order

(ii) Their median is 25

To find: value of x

Solution: Arrange the given terms in ascending order,

we get,

            8,11,12,(2x-8),(2x+10),35,42,50

Since the number of terms are even so median of given terms is average of $\frac{n}{2} ^{th}$ term and $($$\frac{n}{2}+1) ^{th}$ term,

here n = 8, hence median is the average of $4^{th}$ and $5^{th}$ term, given by

           $\frac{2x-8+2x+10}{2}$ $= 25$

$4x + 2=25$×$2$

$4x +2 = 50\\4x= 48\\x=12$

Hence the value of x is 12