Averages from a Grouped Frequency Table
A grouped frequency table sorts data into class intervals and lists their frequencies. A frequency of 8 for 20-30 means 8 values fall in that range. From it you find the modal class, median class, and estimate the mean.
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What Is a Grouped Frequency Table?
- A grouped frequency table organises data into class intervals.
- Each class shows how many values fall within that interval.
How to Find the Modal Class?
- The modal class is the class with the highest frequency.
- It shows where the data occurs most often.
How to Find the Median Class?
- Add the frequencies to find the total number of values (n).
- Use (n + 1) ÷ 2 to find the median position.
- If , , so the class containing the 13th value is the median class.
How to Estimate the Mean?
- Find the midpoint of each class by adding the lower and upper values and dividing by 2.
- Multiply each midpoint by its frequency and add the results.
- Divide this sum by the total frequency to estimate the mean.
Practice Questions
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The table shows the ages of people attending a concert. How many people are represented in total?
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The total number of people is the sum of the frequencies, not of the age labels.
people attended the concert.
The table shows the ages of people attending a concert. What is the modal class for the data?
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The modal class is the group with the highest frequency.
The frequencies are 6, 8, 4 and 2, and the highest is 8, which belongs to the 20-30 years group. So the modal class is 20-30 years.
The table below shows the delivery times for a courier service. Which class contains the median delivery time?
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Total frequency: .
With 20 values, the median lies halfway between the 10th and 11th values. The running totals are 4, then , then 17, then 20.
The 10th and 11th values are both in the second class, so the median lies in 20-30 minutes.
The table below shows the delivery times for a courier service. What is the midpoint of the 20-30 minute class?
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The midpoint of a class is halfway between its two endpoints.
minutes.
The table below shows the delivery times for a courier service. If 2 more orders are added to the 30-40 minute class, how does this affect the modal class?
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The 30-40 class had a frequency of 6. Adding 2 more orders makes it .
The frequencies are now 4, 7, 8 and 3. The highest is 8, so the modal class changes from 20-30 minutes to 30-40 minutes.
The table below shows the delivery times for a courier service. Estimate the mean delivery time.
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Use the class midpoints: 15, 25, 35 and 45 minutes.
Multiply each midpoint by its frequency: .
Divide by the total frequency: minutes.
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Averages from grouped frequency table
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Averages from a Grouped Frequency Table frequently asked questions
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Each row shows a class interval and its frequency. The class interval is a range, such as 10 to 20 minutes. The frequency tells you how many values fall in that range. In the pizza example, a frequency of 4 means 4 deliveries took between 10 and 20 minutes.
Read the frequency column and find the largest frequency. The class interval next to that frequency is the modal class. In the pizza delivery table, the largest frequency is 10. It belongs to the 40 to 50 minutes interval, so that is the modal class.
A grouped frequency table only shows the class each value falls in, not the exact values. Because the exact data is unknown, you use the midpoint of each class to represent it. This gives an estimate of the mean rather than an exact answer.
The midpoint is the value halfway between the two ends of a class interval. For the 10 to 20 minutes class, the midpoint is 15. Midpoints are used to estimate the mean, because the exact values in each class are unknown.
Use the formula (n + 1) ÷ 2, where n is the total frequency. For the pizza table, n is 25. The median position is (25 + 1) ÷ 2 = 13, the 13th value. You then find which class interval contains that position.