Question

Ascending order of a data is given as: 21, 23, 27, 29, x, x + 2, 32, 35, 37, 40. If median of the data is 32, then find the value of x.​

Answer 1

Answer:

The value of x is 31

Step-by-step explanation:

Given Data = 21, 23, 27, 29, x, x + 2, 32, 35, 37, 40.

There are 10 terms (even terms)

We know that

Median = $\frac{1}{2}$ * [$(\frac{n}{2})^{th}$ term + $(\frac{n}{2} + 1)^{th}$ term]

where n is the number of terms

Substituting the values here, we get

=> Median = $\frac{1}{2}$ * [ x + (x+2)]

                  = $\frac{1}{2}$ * [2x + 2]

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

                  = x + 1

Since it is given that median is 32

=> 32 = x + 1

=> 32 - 1 = x

=> x = 31

Therefore the value of x is 31