Last reviewed: 10 November 2026
Updated November 2026. These Grade 9 grouped data notes show how to choose a class width, draw a frequency distribution table, identify the modal class, and calculate the mean and median of grouped data. For the mean, multiply each class midpoint by its frequency, add the results and divide by the total frequency. For the median, find the class containing the middle value and estimate within it.
The examples and questions are original practice for Kenyan junior school learners, not an official paper. For the other Grade 9 maths topics, see our Grade 9 maths revision guide and the Grade 9 notes hub. For ungrouped data, see our mean, median, mode and charts notes.
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What the Grade 9 Curriculum Covers
“Data Interpretation (Grouped Data)” is a sub-strand under Data Handling and Probability in the Kenya Institute of Curriculum Development’s Grade 9 Mathematics design. Learners determine an appropriate class width, draw frequency distribution tables of grouped data, identify the modal class, and calculate the mean and median of grouped data. The design is listed on the KICD Grade Nine curriculum designs page.
Grouping Data and Choosing a Class Width
When there are many different values, list them in classes (groups) instead of one by one. A useful starting point: class width ≈ range ÷ number of classes you want (often 5 to 8), rounded up to a convenient number.
Example: 30 learners’ test marks range from 2 to 48. Range = 46. For 5 classes, 46 ÷ 5 = 9.2, so a width of 10 works: 0–9, 10–19, 20–29, 30–39, 40–49. Classes must not overlap and must cover every value.
Frequency Distribution Table
Tally each value into its class, then count. In this made-up data set:
| Marks | Frequency (f) | Midpoint (x) | fx | Cumulative frequency |
|---|---|---|---|---|
| 0–9 | 3 | 4.5 | 13.5 | 3 |
| 10–19 | 7 | 14.5 | 101.5 | 10 |
| 20–29 | 12 | 24.5 | 294 | 22 |
| 30–39 | 6 | 34.5 | 207 | 28 |
| 40–49 | 2 | 44.5 | 89 | 30 |
| Total | 30 | 705 |
The midpoint is (lower limit + upper limit) ÷ 2, so for 10–19 it is (10 + 19) ÷ 2 = 14.5.
The Modal Class
The modal class is the class with the highest frequency. Here it is 20–29, with 12 learners. With grouped data you name the class, not a single mode, because the exact values are hidden inside the groups.
Mean of Grouped Data
Mean = Σfx ÷ Σf, where Σ means “the sum of”. This follows the method in OpenStax Introductory Statistics’ section on measures of the centre of data, which uses class midpoints to estimate the mean from a frequency table.
Mean = 705 ÷ 30 = 23.5 marks.
This is an estimate: using the midpoint assumes values are spread evenly within each class.
Median of Grouped Data
- Find the position of the middle value: Σf ÷ 2 = 30 ÷ 2 = 15.
- Use the cumulative frequency to find the median class: the 15th value is after 10 and up to 22, so the median class is 20–29.
- Estimate within the class with: median = L + ((n/2 − F) ÷ f) × w, where L is the lower class boundary (19.5), F the cumulative frequency before the class (10), f the class frequency (12) and w the class width (10).
- Median = 19.5 + ((15 − 10) ÷ 12) × 10 = 19.5 + 4.17 ≈ 23.7 marks.
The lower class boundary is halfway between 19 and 20, which is why L = 19.5, not 20. Some teachers accept identifying the median class only; follow the level your teacher sets.
Original Practice Questions With Worked Answers
Use this made-up table of the masses (kg) of 20 learners: 30–34: 2; 35–39: 5; 40–44: 8; 45–49: 4; 50–54: 1.
- State the modal class. 40–44.
- Find the midpoint of 35–39. (35 + 39) ÷ 2 = 37.
- Find the mean. Midpoints 32, 37, 42, 47, 52. Σfx = 64 + 185 + 336 + 188 + 52 = 825. Mean = 825 ÷ 20 = 41.25 kg.
- Find the median class. n/2 = 10. Cumulative frequencies 2, 7, 15… so the median class is 40–44.
- Estimate the median. 39.5 + ((10 − 7) ÷ 8) × 5 = 39.5 + 1.875 ≈ 41.4 kg.
Cover the answers and attempt each question first. For timed practice, use the Grade 9 revision papers or the Grade 9 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
How do you find the mean of grouped data?
Multiply each class midpoint by its frequency, add the products, and divide by the total frequency.
What is the modal class?
The class with the highest frequency in a grouped frequency table.
How do you find the median class?
Divide the total frequency by 2, then use the cumulative frequency column to find the class that contains that position.
How do you choose a class width?
Divide the range of the data by the number of classes you want and round up to a convenient number, making sure classes do not overlap.