Question

The runs scored by a batsman in 10 matches are 34, 65, 23, 11, 28, 56, 87, 54, 98, and 12, respectively.
Finds the median of the runs scored in these 10 matches.

Answer 1

We know that the median of a given set of observation is the value which divides it into two equal parts.

Given that, the number of observations is 10, which is even.

Arranging the runs in ascending order, we get the following order:
11, 12, 23, 28, 34, 54, 56, 65, 87, 98

Now,
$\text{Median}=\frac{{\frac{n}{2}}^{th}term+{(\frac{n}{2}+1)}^{th}term}{2}$

$\text{Median}=\frac{{\frac{10}{2}}^{th}term+{(\frac{10}{2}+1)}^{th}term}{2}$

$\text{Median}=\frac{5^{th}term+6^{th}term}{2}$

$\therefore \text{Median}=\frac{34+54}{2}=44$

Thus, 44 is the median of the runs scored in 10 matches.