Mean From Grouped Frequency Table Example

This document is a step-by-step guide to estimating a mean from a grouped frequency table. Can be given to students as a worked example or revision tool.

How to Work Out the Mean from a Frequency Table

The concept of mean from a frequency table is an important and common statistical method for KS3 and KS4 curriculum. This concept is generally used to find the average of grouped data. Our statistics teaching resource- ‘Mean From Grouped Frequency Table Example’ will help you teach and understand how to find the mean of a frequency table, as well as grouped and ungrouped frequency tables, with easy-to-understand, step-by-step explanations.

What is a Frequency Table?

A frequency table is commonly used for organizing data into categories. It shows how often each value or group of values appears in a statistical calculation. When the data is grouped, we must use midpoints to calculate the mean.

How to Find the Mean of a Frequency Table (Step-by-Step)

To find the Mean of a Frequency Table, we will use the mean formula. That is-

Mean=∑fx∑f\text{Mean} = \frac{\sum fx}{\sum f}Mean=∑f∑fx​

Where:

• fff = frequency (number of occurrences)
• xxx = midpoint of each class interval
• fxfxfx = frequency multiplied by the midpoint

Example: Mean from a Grouped Frequency Table

For example, let’s imagine a teacher is recording the ages of students in a frequency table:

Step 1: Find the Midpoints

The midpoint of each class can easily be calculated as:

Midpoint=Lower Bound+Upper Bound2\text{Midpoint} = \frac{\text{Lower Bound} + \text{Upper Bound}}{2}Midpoint=2Lower Bound+Upper Bound​

Step 2: Multiply Frequency by Midpoint (fx)

Multiply each frequency by its corresponding midpoint.

∑fx=1215\sum fx = 1215∑fx=1215

Step 3: Find the Total Frequency

Sum up all the frequencies:

12+25+37+14=8812 + 25 + 37 + 14 = 8812+25+37+14=88 ∑f=88\sum f = 88∑f=88

Step 4: Divide the Total fx by the Total Frequency

Using the mean formula:

Mean=∑fx∑f=121588=13.8\text{Mean} = \frac{\sum fx}{\sum f} = \frac{1215}{88} = 13.8Mean=∑f∑fx​=881215​=13.8

Final Answer: The mean age is 13.8 years.

Key Takeaways 

 Here are some key takeaways that you must remember- 

1. We must use midpoints when working with grouped frequency tables.
2. We need to multiply frequency by midpoint, then sum the totals.
3. It must be divided by the total frequency to get the mean.