Question

Question 4
A football player scored the following number of goals in the 10 matches.
1, 3, 2, 5, 8, 6, 1, 4, 7 and 9.
Since the number of matches is 10 ( an even number),
$\text{Median}=\frac{\text{5th observation + 6th observation}}{2}=\frac{8+6}{2}=7$
Is it the correct answer and why?

Answer 1

No, It is not the correct answer, because the data have to be arranged in ascending or descending order before finding the median.

Arranging the data in ascending order 1, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Here, the number of observations is 10, which is even.

So, median=$\frac{(\frac{n}{2}th\text{observation}+(\frac{n}{2}+1)th\text{observation})}{2}$

$=\frac{(\frac{10}{2}th\text{observation}+(\frac{10}{2}+1)th\text{observation})}{2}$

$=\frac{5th\text{observation}+6th\text{observation}}{2}=\frac{4+5}{2}=\frac{9}{2}=4.5$