Question

Find the MEDIAN of the data set. (Hint: the numbers must be in order first!) 40 76 40 63 47 57 49 55 50 53

Answer 1

Given:

The data set is:

40, 76, 40, 63, 47, 57, 49, 55, 50, 53

To find:

The median of the given data set.

Solution:

We have,

40, 76, 40, 63, 47, 57, 49, 55, 50, 53

Arrange the data values in ascending order.

40, 40, 47, 49, 50, 53, 55, 57, 63, 76

Here, the number of observations is 10 which is an even number. So, the median is:

$Median=\dfrac{(\dfrac{n}{2})\text{th term}+(\dfrac{n}{2}+1)\text{th term}}{2}$

Putting n=10, we get

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

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

From the arranged terms, it is clear that the the 5th term is 50 and the 6th term is 53.

$Median=\dfrac{50+53}{2}$

$Median=\dfrac{103}{2}$

$Median=51.5$

Therefore, the median of the given data set is 51.5.