Question

A) Find the median of the following observations arranged in the ascending order:

8,11, 13, 15, x + 1, x + 3, 30, 35, 40, 43 is 22. Find the value of x.

Answer 1

x = 20

Explanation:

Median:

`\sf \text{\bf Number of data is 10. So the median will be the average of $n^(th) and (n+1)^(th) term $ }`

Median = average of 5th and 6th term

`\sf = ((x +1) + (x+ 3))/(2)\\\\ =(x +x + 1 + 3)/(2)\\\\= (2x + 4)/(2)`

It is given that median = 22

`\sf (2x + 4)/(2)= 22\\\\2x + 4 = 22*2\\\\2x + 4 = 44`

2x = 44 - 4

2x = 40

x = 40/2

`\sf \boxed{x = 20}`