Question

How to find the mean, mode and median of a set of numbers?

Answer 1

Step 1: Define the set of numbers.

Suppose we have $n$ values in a set of data namely $x_1,x_2,.....,x_n$.

Step 2: Find the mean of a set of numbers

The mean of the given data is given by

$\overline{x}=\frac{x_1+x_2+....+x_n}{n}=\frac{1}{n}\underset{i=1}{\overset{n}{\sum x_i}}$

Step 3: Find the median of a set of numbers

Generally median represents the mid-value of the given set of data when arranged in a particular order.

Given that the set of data is arranged in ascending or descending order, then the following method is applied

1. If the number of values or observation in the given set of data is odd, then the median is given by ${\left(\frac{n+1}{2}\right)}^{th}$observation
2. If the number of values or observation in the given set of data is even, then the median is given by ${\left(\frac{n}{2}\right)}^{th}$and ${\left(\frac{n}{2}+1\right)}^{th}$observation

In a group of data median is calculated by

$\mathrm{Median}=\mathrm{l}+\left[\frac{{\displaystyle \frac{\mathrm{n}}{2}}-\mathrm{c}}{\mathrm{f}}\right]\times \mathrm{h}$

where $l=$lower limit of median class, $n$ number of observation ,$c$ cumulative frequency of preceding class,$f$ frequency of each class and $h$ is the class size.

Step 4: Find the mode of a set of numbers

The most frequent number in the data set is known as mode.

For a group of data mode is calculated by

$\mathrm{Mode}=\mathrm{l}+\left[\frac{{\mathrm{f}}_1-{\mathrm{f}}_0}{2{\mathrm{f}}_1-{\mathrm{f}}_0-{\mathrm{f}}_2}\right]\times \mathrm{h}$

Where,$l=$ lower class limit of modal class,$h=$class size,$f_1=$frequency of modal class,$f_0=$ frequency of class proceeding to modal class,$f_2=$ frequency of class succeeding to modal class.

Hence, with the following method we can find mean, median and mode.