Question

How do you find the mean and median of the data set:

There are $28,30,29,26,31,\mathrm{and}30$ students in a school's six Algebra l classes?

Answer 1

Step 1. Finding the mean of the data set:

Let, the mean is $\alpha$.

When calculating the mean of a set of data, add up all the values and divide that total by the number of data points.

$\begin{array}{rcl}\alpha & =& \frac{28+30+29+26+31+30}{6}\\ & =& \frac{174}{6}\\ & =& 29\end{array}$

Step 2. Finding the median of the data set:

Let, the median is $\beta$.

Calculating the median, first convert this data set in ascending order first.

The ascending order is $26,28,29,30,30,31$.

Now, looking for the middle term in the ordered set:

If the number of all data is odd, then there is only one such number.

If the number of all data is even, then there are two such numbers, find the mean of these two numbers.

This set of data have $6$ elements, so there are $2$ middle numbers.

The two middle numbers are $29,30$ .

$\begin{array}{rcl}\beta & =& \frac{29+30}{2}\\ & =& \frac{59}{2}\\ & =& 29.5\end{array}$

Hence, the mean of the data set is $29$ and the median of the data set is $29.5$.