Arithmetic Mean for Grouped Data

Topics: Arithmetic Mean - Statistics

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(definition)

Let $f_1,\dots ,f_n$ be the frequencies of a variable $X$ and let $c_1,\dots ,c_n$ be class marks. Then:

$$\mathrm{Mean}(X)=\frac{{\sum }_{i=1}^n{f}_i{c}_i}{{\sum }_{i=1}^n{f}_i}$$

Example

For instance, let’s say we have the following group of data, concerning the age of a group of people:

Class (age)	Frequency
Adult	25
Senior	10

We have no data about the actual age of each one of those people, but nevertheless, we’ll use what we know to calculate the mean of these people’s age.

First, we know that the age of an adult is between 20 and 65. The average of these two values is 42.5, so we’ll set 42.5 as the mark class for the adult class.

Similarly, the age of a senior is between 66 and (let’s say) 100. The average of these two values is 83, so we’ll set 83 as the mark class for the senior class.

We can calculate the mean by using the formula given above, now that we have set our class marks.