Question

What are the Mean and Median?

Answer 1

Mean:

The mean of the data set is the arithmetic average or the ratio of the sum of the elements to the total number of elements of a set.

Formula: $\mathbf{\text{Mean =}}\frac{\mathbf{Sum}\mathbf{}\mathbf{of}\mathbf{}\mathbf{elements}}{\mathbf{Total}\mathbf{}\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{elements}}$

Median:

The median is the middle value of the data set when arranged in an ascending or descending order.

When there is an odd number of elements in a data set: $\mathbf{Median}\mathbf{=}{\left(\frac{n+1}{2}\right)}^{\mathbf{th}}$term

When there is an even number of elements in a data set: $\mathbf{Median}\mathbf{=}\left[\frac{{\left(\frac{n}{2}\right)}^{\mathrm{th}}\mathrm{term}+{\left(\frac{n}{2}+1\right)}^{\mathrm{th}}\mathrm{term}}{2}\right]$

Example: $1,2,6,7,4,3,5,3,2,8$

Number of elements present in a set $=10$

Then, the mean of the set is

$Mean=\frac{1+2+6+7+4+3+5+3+2+8}{10}$

$\Rightarrow$ $Mean=\frac{41}{10}$

$\Rightarrow$ $Mean=4.1$

There is an even number of elements in a data set

Arranged data set: $1,2,2,3,3,4,5,6,7,8$

Then, the median of the set is,

$\mathbf{Median}\mathbf{=}\left[\frac{{\left(\frac{10}{2}\right)}^{\mathrm{th}}\mathrm{term}+{\left(\frac{10}{2}+1\right)}^{\mathrm{th}}\mathrm{term}}{2}\right]$

$\Rightarrow$ $Median=\left[\frac{5^{th}term+6^{th}term}{2}\right]$

$\Rightarrow$ $Median=\frac{3+4}{2}$

$\Rightarrow$ $Median=\frac{7}{2}$

$\Rightarrow$ $Median=3.5$