# The median of the numbers 84, 78, 54, 56, 68, 22, 34, 45, 39, 54 is

Question:

The median of the numbers 84, 78, 54, 56, 68, 22, 34, 45, 39, 54 is
(a) 45
(b) 49.5
(c) 54
(d) 56

Solution:

(c) 54

We will arrange the data in ascending order as:
22, 34, 39, 45, 54, 54, 56, 68, 78, 84
Here, n is 10, which is an even number.
Thus, we have:

Median $=$ Mean of $\left(\frac{n}{2}\right)$ th & $\left(\frac{n}{2}+1\right)$ th observations

$=\frac{1}{2}$ (5 th observation $+6$ th observation)

$=\frac{1}{2}(54+54)=54$