Analysing grouped frequency tables
When data is grouped into classes – like height ranges or time intervals – we lose the exact values, but we can still estimate the mean, median, and mode. These estimates help us understand the typical or average values in large data sets, which is especially useful in real-world situations like analysing survey results, planning bus timetables, or tracking fitness progress. Jump to the questions
Practise now
Identify the modal class, the median class, and estimate the mean.
Topic guide
What this worksheet practises
This worksheet practises estimating the mean from a grouped frequency table. When data is grouped into classes (e.g., 10 < x ≤ 20), we lose the exact individual values. Therefore, we can only ever calculate an estimate of the mean.
Key method
To estimate the mean, you use the midpoint of each class interval to represent all the values in that group.
- Find the midpoint of each class interval by adding the lower and upper bounds together and dividing by two.
- Multiply the midpoint by the frequency for that row.
- Add up all the frequencies to find the total number of items.
- Add up all the (Midpoint × Frequency) values to find the estimated total sum.
- Divide the estimated total sum by the total frequency.
Worked example
Estimate the mean time taken from the table below:
- 0 < t ≤ 10: frequency = 2
- 10 < t ≤ 20: frequency = 3
Step 1: Find the midpoints. For 0-10 it is 5. For 10-20 it is 15.
Step 2: Multiply midpoints by frequencies.
- 5 × 2 = 10
- 15 × 3 = 45
Step 3: Find the total frequency: 2 + 3 = 5.
Step 4: Find the estimated total sum: 10 + 45 = 55.
Step 5: Divide sum by frequency: 55 ÷ 5 = 11.
The estimated mean time is 11.
Things to remember
Always verify your answer makes sense. The estimated mean must fall somewhere within the range of your groups. If your groups span from 0 to 20, and your answer is 45, you know a calculation error has occurred.