Arithmetic mean, median and mode are three different way to describe a set of data quantitatively. Here we have the definition for each one:

Arithmetic mean (Average): In a set of $n$ measurements, the sum of the measurements divided by $n$.

$Mean$ = $\frac{Sum\ of\ the\ terms}{Number\ of\ terms}$$\frac{a+b+c+.......+n^{th} term}{n}$

Median: This is the middle measurement after all the measurements are arranged by size (or the average of the two middle measurements if the number of measurements is even).

The measurement that appears most frequently in a set.     

For example, given a set of six measurements $(9,-4,9,3,2,8)$:
$Mean$ = $\frac{9-4+9+3+2+8}{6}$ = $\frac{27}{6}$ = $4.5$

Order the data in assenting order $-4,2,3,8,9,9$
$Median$ = $5.5$, (The average of $3$ and $8$)

$Mode$ = $9$, ($8$ appears twice, more frequently than any other measurement)
For the same set of values, the mean and the median can be same, but not necessarily. For example (2,3,4,5,6)  has both mean and median of $4$. However, the set $(9,-4,9,3,2,8)$ has a mean of $4.5$ but a median of $5.5$.
Mean Median Mode Calculator is an online tool which will help us to calculate the mean, median and mode of any set of data.      

The following are the steps to calculate the mean, median and mode of any set of data. 

Step 1: To find the mean of given data, divide the sum of all data with total number of data.

Step 2: Arrange the given set of data in ascending or descending order.

Step 3: Median is the middle data after after all the data arranged by size.

Step 4: The data that appears most frequently is the mode.