Question

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

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

Answer 1

Step-1. Find the value of the Mean:

Given, the data set is $26,28,29,30,30,31$

The sum of all the values in a data set must be divided by the total amount of data in order to determine the mean:

$\begin{array}{rcl}\text{Mean}& =& \frac{\sum x_i}{n}\\ & \Rightarrow & \text{Mean}=\frac{x_1+x_2+x_3+\dots +x_n}{n}\\ & \Rightarrow & \text{Mean}=\frac{28+30+29+26+31+30}{6}\\ & \Rightarrow & \text{Mean}=\frac{174}{6}=29\end{array}$

Step-2: Find the value of the Median:

The set of data will be arranged in ascending order for that purpose.

The data set is $26,28,29,30,30,31$.

The middle term in the ordered set must now be found.
There is only one such number if all the data are odd; otherwise, there are two such numbers.

First, we can apply the formula or the middle term in the ordered set $\mathrm{Term}=\frac{n+1}{2}$ to find the term of the given set.

In the second scenario, finding the mean of the middle two numbers is necessary to get the median.

Alternatively, we can apply the formula $\mathrm{Term}=\frac{n}{2},\frac{n}{2}+1$to determine the mean of these two terms.

There are two middle numbers from the supplied set of data$\left(26,28,29,30,30,31\right)$ as $29$ and $30$ because this set comprises $6$ items.
In order to get the median, we will first find the mean of $29$ and $30$:

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

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