Question

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

(a) 45
(b) 49.5
(c) 53.5
(d) 56

Answer 1

Disclaimer: Options (d) in the question changed to match the answer.

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

(a) 45
(b) 49.5
(c) 53.5
(d) 54

Solution:

Arranging the data in ascending order, we have

22, 34, 39, 45, 54, 54, 56, 68, 78, 84

Here, the number of observations n = 10, which is even

∴ Median of the data

= $\frac{\mathrm{Value}\mathrm{of}\left({\displaystyle \frac{10}{2}}\right)\mathrm{th}\mathrm{observation}+\mathrm{Value}\mathrm{of}\left({\displaystyle \frac{10}{2}}+1\right)\mathrm{th}\mathrm{observation}}{2}$

= $\frac{\mathrm{Value}\mathrm{of}5\mathrm{th}\mathrm{observation}+\mathrm{Value}\mathrm{of}6\mathrm{th}\mathrm{observation}}{2}$

= $\frac{54+54}{2}$

= $\frac{108}{2}$

= 54

Thus, the median of the given data is 54.

Hence, the correct answer is option (d).