Question

The following observations have been arranged in ascending order. If the median of the data is 78, find the value of x.
44, 47, 63, 65, x + 13, 87, 93, 99, 110.

Answer 1

Consider the given data :
44, 47, 63, 65, x + 13, 87, 93, 99, 110
Here the number of observations is 9, which is odd.

Thus, the median of the given data is `([n + 1 ]/2)^"th"` observation.

From the given data, `([9 + 1 ]/ 2 = 5)^"th"` observation is x + 13
Also, given that the median is 78.
x + 13 = 78
⇒ x = 78 - 13
⇒ x = 65