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Arithmetic mean of grouped data calculator

With this statistical calculator, you will learn how to calculate the arithmetic mean of a distribution point series (grouped data).

To get the result, enter the values and their frequency.

Arithmetic mean of the distribution point series (grouped data)

Arithmetic mean grouped data - information

Formula used to calculate the arithmetic mean of the point distributing series (grouped data):

$$\bar{x}=\frac{f_1·x_1+f_2·x_2+\cdots+f_n·x_n}{f_1+f_2+\cdots+f_n}=\frac{\sum{f\,x}}{\sum{f}}$$ where:
x - grouped data
f - frequency

EXAMPLE
We are looking for the arithmetic mean for 4,6,8,6,8,4,6.

The arithmetic mean will be $\frac{4+6+8+6+8+4+6}{7}=\frac{42}{7}=6$

However, sometimes we have data already grouped or for statistical purposes we need to present them in groups.
From our example, we can create the following groups:
group of fours - frequency 2;
group of sixes - frequency 3;
group of eighth - frequency 2.

So in the example above we have two fours, two eights and three sixes.
The frequency (f) is the number of occurrences of an element in its group.

For a better understanding, let's present it in the form of a table:

Data (X)	Frequency (f)	$X·f$
4	2	4 · 2 = 8
6	3	6 · 3 = 18
8	2	8 · 2 = 16
	$\sum{f}$ = 7	$\sum{f\,x}$ = 42

Substituting into the formula we can calculate the arithmetic mean.

$$\bar{x}=\frac{\sum{f\,x}}{\sum{f}}=\frac{42}{7}=6$$

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