How to Find Mean of a Grouped Frequency Table

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If you have organized your observations in a frequency table, you can find the mean directly from the table without writing it out as a long list of numbers. Here you’ll learn how.

Rule

Mean: Grouped Data with Known Frequencies

You multiply every observational value xi by its frequency fi, add them together, then divide by the total number of observations:

Mean = x1f1 + x2f2 + + xnfn Number of observations

Here’s the rule with a more theoretical approach:

Rule

Mean: Grouped Data with Known Frequencies

Multiply every observational value xi by its frequency fi, then divide the sum of these values by the total number N = fi of observations.

x = x1f1 + x2f2 + + xnfn N

Example 1

Below is an example of a table of frequencies. A class of 20 students had a test in mathematics. Their grades were as follows:



Grade Frequency


0 1


1 2


2 3


3 7


4 7


Total 20


Find the mean grade.

x = 0 1 + 1 2 + 2 3 + 3 7 + 4 7 20 x = 57 20 x = 2.85

The mean grade of the class was 2.85.

Mean: Grouped Data with Known Relative Frequency

If you have a table of frequencies but only know the relative frequencies, you can find the mean in the following way:

Theory

Mean: Grouped Data With Known Relative Frequency

Multiply each point with its relative frequency r = f n, where f is the frequency and n is the total number of observations, and add all these values together.

x = x1r1 + x2r2 + + xnrn

Example 2

A school of 974 students has given you a table containing relative frequencies of the grades its students have achieved in Latin, and have asked you to find the mean Latin grade.



Grade Relative Frequency


0 49 974 = 0.050


1 78 974 = 0.080


2 304 974 = 0.312


3 306 974 = 0.314


4 237 974 = 0.243


Total 1


x = 0 49 974 + 1 78 974 + 2 304 974 + 3 306 974 + 4 237 974 = 2.62

x = 0 49 974 + 1 78 974 + 2 304 974 + 3 306 974 + 4 237 974 = 2.62

The school’s mean grade in Latin is 2.62.

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