### Mean

The mean of a given set of numbers is the average of those numbers, and is calculated by summing all the numbers and dividing by the amount of numbers.

That is, the mean =

Example:

Find the mean of the following numbers:

6, 12, 15, 20, 14, 8, 10, 18, 24, 12

To find the mean of a frequency distribution with ungrouped data, the product of the frequency and the corresponding observations (noted as fx) is calculated and summed, that sum is then divided by the sum of the frequency amounts.

That is, the mean

=Ʃ*f*x

Ʃ*f*

Where, Ʃ*f*x is the sum of the products of the frequency and the corresponding observations

And, Ʃf is the sum of the frequencies.

Example:

The table below shows the size show a survey of 50 men wear.

Find the mean size show.

Procedure to find the mean:

-Multiply the frequencies by the corresponding observations.

-Sum the product of the frequencies and the observations.

-Sum the frequencies.

-Divide the sum of the products of the frequencies and observations by the sum of the frequencies.

Therefore, Ʃ*f*x = 510

And, Ʃf = 50

That is, the mean

To find the mean of a frequency distribution with grouped data, firstly find the mid-point of each class interval, then find the product of the frequency and the corresponding mid-points (noted as f_{1} x_{1}) and sum them, that sum is then divided by the sum of the frequency amounts.

That is, the mean

=Ʃ*f _{1}*x

_{1}

Ʃ*f _{1}*

Where, Ʃ*f _{1}*x

_{1}is the sum of the products of the frequency and the corresponding mid-points

And, Ʃf_{1} is the sum of the frequencies.

Example:

Find the mean of the following data.

Procedure to find the mean:

-Find the mid-point of each class by adding the lower class limit and the upper class limit of each class, and dividing by two.

-Multiply the mid-points of each class by the respective frequencies.

-Sum the product of the mid-points and the frequencies.

-Sum the frequencies.

-Divide the sum of the products of the mid-points and the frequencies by the sum of the frequencies.

Therefore, Ʃ*f _{1}*x

_{1}= 4095

And, Ʃf_{1} = 71

That is, the mean