Question

Question 21
The median of the data 78, 56, 22, 34, 45, 54, 39, 68, 54 and 84 is:

A) 45
B) 49.5
C) 54
D) 56

Answer 1

The answer is C.
First, we arrange the given observations in ascending order as follows.
22, 34, 39, 45, 54, 54, 56, 68, 78 and 84
Here, total number of observations, n = 10
Since n is even, we use the formula for the median.

$\text{Median}=\frac{\left(\frac{n}{2}\right)th\text{observation}+(\frac{n}{2}+1)th\text{observation}}{2}$
$=\frac{\left(\frac{10}{2}\right)th\text{observation}+(\frac{10}{2}+1)th\text{observation}}{2}$ [put n = 10]

$=\frac{5th\text{observation}+6th\text{observation}}{2}=\frac{54+54}{2}=\frac{108}{2}=54$

Hence, the median of given data is 54.