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.

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

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