Question

The numbers 6, 8, 10, 12, 13 and x are arranged in an ascending order. If the mean of the observations is equal to the median, find the value of x.

Answer 1

The numbers are 6, 8, 10, 12, 13 and x

Mean = `(6 + 8 + 10 + 12 + 13 + x)/(6)`

Mean = `(49 + x)/(6)`   ...(1)

For Median

n = 6  ...(Even)

Median = `((n/2)^(th) term + (n/2 + 1)^(th) term)/(2)`

∴ Median = `(3^(rd)  term + 4^(th)  term)/(2)`

= `(10 + 12)/(2)`

= `(22)/(2)`

= 11       ...(2)

From (1) and (2) (From question)

Median = Mean

∴ `11 = (49 + x)/(6)`

`=>` x = 66 – 49

`=>` x = 17