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

Given data in ascending order: 6, 8, 10, 12, 13, x

Total number of observation = N = 6 (even)

:. Median = `((N/2)^"th" term + (N/2 +1)^"th" term)/2`

`= ((6/2)^"th" term + (6/2 + 1)^"th" term)/2`

`= ("3 rd term +  4th term")/2`

`= (10 + 12)/2`

`= 22/2`

= 11

Now, Mean = `(6 + 8 + 10 + 12 + 13 + x)/6 = (49 + x)/6`

It is given that 

Mean = Median

`=> (49 + x)/6 = 11`

`=> 49 + x = 66`

`=> x = 17`