Question

5. If the median of the observations arranged in the ascending order as 6, 7, x-2,
x, 17,20 is 16, then x = .........​

Answer 1

Total no. of observations(n)=6

Median = 16

median for even no. of observations={n/2+1}th observation + {n/2}th observation× 1/2

we know that 6/2=3rd observation =x-2

also 3rd+ 1= 4th observation = x

therefore median={(x-2)+(x)}(1/2)

16=(2x-2)1/2

16 × 2 = 2(x-1)

32/2=x-1

16=x-1

x=16+1

x=17

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