How to Calculate the Mean of Grouped Data – Statistics

How to Calculate the Mean of Group Data from a Frequency Distribution Table

Understanding the Frequency Distribution Table

• The lesson introduces calculating the mean of group data using a frequency distribution table, which displays students' scores in a statistics test.

• The first column lists class intervals (score ranges), while the second column indicates frequency, showing how many students scored within each interval.

Calculating Midpoints

• The midpoint for each class is calculated as the average of its lower and upper limits. For example, for the first class (50-59), it is calculated as (50 + 59) / 2 = 54.5.

• Similarly, for the second class (60-69), the midpoint is calculated as (60 + 69) / 2 = 64.5. This process continues for all remaining classes.

Multiplying Midpoints by Frequencies

• Each midpoint is multiplied by its corresponding frequency:

• First class: 6 times 54.5 = 327

• Second class: 10 times 64.5 = 645

• This multiplication is repeated for all classes to obtain products that will be summed up later.

Summing Products and Frequencies

• After multiplying midpoints by frequencies, all products are summed to get a total of 2,980.

• Additionally, summing all frequencies gives a total number of students equal to 40.

Final Calculation of Mean

• To find the mean test score, divide the sum of products (2,980) by total frequency (40), resulting in an estimated mean score of 74.5.

• It’s important to note that this mean is an estimate since exact individual scores are unknown; only ranges and frequencies are available.