Question

the median of the following observations arranged in ascending order
13,15,17,21,x+2,x+4,32,37,41 and 48 is 27.find x

Answer 1

no, of observations= 10 (even)

So, median= [tex] (\frac{n}{2}th + \frac{n+1}{2} th)/2=(5th+6th)/2=x+2+x+4/2= \frac{2x+6}{2} =27 \\ 2x+6=54 \\ 2x=48 \\ x=24 [/tex]

Answer 2

Since the number of observations is even, the median will be the mean of the n/2 th + the (n/2 + 1) th terms.
= the mean of x+2 and x+4
= {(x+2) + (x+4) }/2
= x+3
Given, x+3 = 27
Thus x = 27-3 = 24