Question

The mean of following numbers is 68. Find the value of ‘x’. 45, 52, 60, x, 69, 70, 26, 81 and 94. Hence, estimate the median.

Answer 1

Mean = `"Sum of all observations"/"Total number of observations"`

∴ `68 = (45 + 52 + 60 + x + 69 + 70 + 26 + 81 + 94)/9`

`=> 68 = (497 + x)/9`

`=>` 612 = 497 + x

`=>` x = 612 – 497

`=>` x = 115

Data in ascending order

26, 45, 52, 60, 69, 70, 81, 94, 115

Since the number of observations is odd, the median is the `((n + 1)/2)^(th)` observation

`=>` Median = `((9 + 1)/2)^(th)` observation = 5th observation.

Hence, the median is 69