http://www.ck12.org Chapter 5. Measures of Central Tendency
5.3 Grouped Data to Find the Mean
Here you’ll learn how to organize and use a frequency distribution table to calculate the mean or average of a set of
data that is grouped in intervals.
On a timed math test, students solved a particular problem at different rates of time. Five students solved the problem
within 1-3 minutes, six of them solved it within 4-6 minutes, ten of them solved it within 7-9 minutes, and three of
them solved it within 10-12 minutes. How could you organize this data into a frequency distribution table and find
out the average time it took to solve this problem?
Watch This
First watch this video to learn about finding the mean of grouped data.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter5GroupedDatatoFindtheMeanA
Then watch this video to see some examples.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter5GroupedDatatoFindtheMeanB
Guidance
All of the values for the means that you have calculated so far have been for ungrouped, or listed, data. A mean can
also be determined forgrouped data, or data that is placed in intervals. Unlike listed data, the individual values for
grouped data are not available, and you are not able to calculate their sum. To calculate the mean of grouped data,
the first step is to determine the midpoint of each interval, or class. These midpoints must then be multiplied by the
frequencies of the corresponding classes. The sum of the products divided by the total number of values will be the
value of the mean.
In other words, the mean for a population can be found by dividing∑m fbyN, wheremis the midpoint of the class
andfis the frequency. As a result, the formulaμ=∑Nm fcan be written to summarize the steps used to determine
the value of the mean for a set of grouped data. If the set of data represented a sample instead of a population, the
process would remain the same, and the formula would be written asx=∑m fn.
The following examples will show how the mean value for grouped data can be calculated.