Theory:

Arithmetic Mean or Mean is defined as the sum of all the observations divided by the total number of observations. It is usually denoted by \(\overline X\).
 
Therefore, mean \(\overline X = \frac{\text{Sum of all the observations}}{\text{Total number of observations}}\)
Arithmetic mean or mean is the commonly used method to find the average of the given data.
Methods of finding mean
  • If the given collection of data is ungrouped, then the mean is obtained by direct method.
 
Mean \(\overline X\) =x1+x2+...+xnn
 
If the number of observations is very long, it is a bit difficult to write them. Hence, we use the Sigma notation \(\sum\) for summation.
 
That is, X¯=i=1nxin, where \(n\) is the total number of observations.
  • If the given collection of data is grouped, then the mean is obtained by the following methods.
 
1. Direct Method:
 
The formula for finding the arithmetic mean using the direct method is given by:
 
X¯=i=1nxifii=1nfi
 
Click here! To recall the direct method to find mean.
 
2. Assumed Mean Method:
 
The formula for finding the arithmetic mean using the assumed mean method is given by:
 
X¯=A+i=1nfidii=1nfi where  \(d_{i} =  x_{i} - A\). 
 
Click here! To recall the assumed mean method to find mean.
 
3. Step Deviation Method:
 
The formula for finding the arithmetic mean using the step deviation mean method is given by:
 
X¯=A+c×i=1nfidii=1nfi where  \(d_{i} = \frac{ x_{i} - A}{c}\). 
 
Click here! To recall the step deviation method to find mean.