Question

The median of the following even numbered data set is .

$36$

$46$

$23$

$19$

$25$

$40$

Answer 1

The steps to determine the median of an even numbered data set are as follows:

Step 1 :

First, we arrange the data set in ascending order.

$19$

$23$

$25$

$36$

$40$

$46$

Step 2 :

As the number of data points in the given data set is $6$, which is even, we get two middle values, $25$ and $36$.

$19$

$23$

$\underset{–}{25}$

$\underset{–}{36}$

$40$

$46$

To find the median, we need to take the mean of two middle values.

$\therefore$ Median= Mean of $25$ and $36$
$=\frac{25+36}{2}=\frac{61}{2}=30.5$

$\therefore$ Hence, the median of the given data set is $30.5$.