# Summary

The calculation of arithmetic mean can be studied under two broad categories:
1. Arithmetic Mean for Ungrouped Data.
2. Arithmetic Mean for Grouped Data.

# Arithmetic Mean for Series of Ungrouped Data

Direct Method
Arithmetic mean by direct method is the sum of all observations in a series divided by the total number of observations.

Assumed Mean Method
If the number of observations in the data is more and/or figures are large, it is difficult to compute arithmetic mean by direct method.

Step Deviation Method
The calculations can be further simplified by dividing all the deviations taken from assumed mean by the common factor 'c'. The objective is to avoid large numerical figures, i.e., if

d = X - A is very large, then find d'.

This can be done as follows:

The formula is given below:
= A +

# Calculation of arithmetic mean for Grouped data Discrete Series

Direct Method
In case of discrete series, frequency against each of the observations is multiplied by the value of the observation. The values, so obtained, are summed up and divided by the total number of frequencies.

Symbolically,

Where, = sum of product of variables and frequencies.
= sum of frequencies.

Quartiles
Quartiles are the measures which divide the data into four equal parts, each portion contains equal number of observations.