Question

find x if the median of the observation in ascending order 24, 25, 26, x+2, x+3, 30, 31, 34 is 27.5

Answer 1

here n is even as there are 8 observations.

so the median is (n/2), (n/2+1)

(8/2),(8/2+1)⇒4,5

the 4th observation is x+2,and the 5th observation is x+3.

if there are two median then we have to take average for the two observations.

so,x+2+(x+3)÷2=27.5

2x+5÷2=27.5

2x+5=27.5×2

2x+5=55

2x=55-5

2x=50

therefore,x=25

Answer 2

median=x+2+x+3/2
x+2+x+3/2=27.5 (given)
x+2+x+3=55
2x+5=55
2x=50
x=25