Finding Mean

Generally, we could find the mean of a data set by using the following formula,

Mean, \(\bar{x}=\frac{\mathrm{Sum \ of \ data}}{\mathrm{Number \ of \ data}}=\frac{\sum{fx}}{\sum{f}}\)

Finding Mean of a Frequency Distribution

For a data set of \({{x}_{1}}\), \({{x}_{2}}\), \({{x}_{3}}\), …, \({{x}_{n}}\), with the corresponding frequencies \({{f}_{1}}\), \({{f}_{2}}\), \({{f}_{3}}\) , …, \({{f}_{n}}\) is usually represented in the form of a frequency table below,

the above equation can be further written as

Mean, \(\bar{x}\) = \(\frac{\sum{fx}}{\sum{f}}=\frac{{{f}_{1}}{{x}_{1}}+{{f}_{2}}{{x}_{2}}+{{f}_{3}}{{x}_{3}}+...+{{f}_{n}}{{x}_{n}}}{{{f}_{1}}+{{f}_{2}}+{{f}_{3}}+...+{{f}_{n}}}\)

The symbol \(\sum{{}}\)(sigma) is used to denote the sum of multiple terms.

Example: Finding Mean of a Frequency Distribution

The monthly salaries of the employees in a company are shown in the table below.

Find the mean monthly salary of the employees.