Grade 7 Mathematics DATA HANDLING AND PROBABILITY – Data handling Notes
Mathematics — DATA HANDLING
Topic: DATA HANDLING AND PROBABILITY • Subtopic: Data handling • Age: 12 (Kenya)
1. What is data handling?
Data handling is the process of collecting information (data), organising it, showing it using tables or pictures and using it to answer questions. Example: A teacher asks 30 pupils their favourite fruit and uses the answers to make a chart.
2. Steps in data handling
- Ask a question (e.g. "Which sport do you like most?").
- Collect data (survey the class).
- Organise data (tally marks, frequency table).
- Represent data (bar graph, pictogram, pie chart).
- Interpret data (answer questions) and calculate simple statistics.
3. Example: Favourite fruits (class survey)
A class of 30 pupils was asked: "Which fruit do you like best?" The answers were recorded as follows and converted to a tally and frequency table.
Tally
| Fruit | Tally | Frequency |
|---|---|---|
| Banana | |||| |||| || | 12 |
| Mango | |||| |||| | 8 |
| Apple | |||| | | 6 |
| Avocado | ||| | 3 |
| Total | 30 |
Pictogram
(Each 🍌 = 2 pupils)
Banana: 🍌🍌🍌🍌🍌🍌 (=12)
Mango: 🍍🍍🍍🍍 (=8) (used 🍍 for mango)
Apple: 🍎🍎🍎 (=6)
Avocado: 🥑🥑 (≈3 shown as 1.5—explain half-symbol if needed)
Mango: 🍍🍍🍍🍍 (=8) (used 🍍 for mango)
Apple: 🍎🍎🍎 (=6)
Avocado: 🥑🥑 (≈3 shown as 1.5—explain half-symbol if needed)
4. Bar graph (visual)
A bar graph helps us compare amounts easily.
Tip: The height of each bar shows how many pupils chose each fruit.
5. Simple statistics: Mean, Median, Mode and Range
We use these to describe a set of numbers (e.g. test scores).
Example — Test scores (out of 100) for 7 pupils:
65, 70, 80, 65, 90, 75, 70
- Mean (average): Add all scores and divide by the number of pupils.
Sum = 65+70+80+65+90+75+70 = 515. Number = 7. Mean = 515 ÷ 7 = 73.6 (about 74).
- Median (middle value): Put scores in order and take the middle one.
Ordered: 65, 65, 70, 70, 75, 80, 90 → middle (4th) = 70. Median = 70.
- Mode (most frequent): The score that appears most often.
65 appears twice, 70 appears twice → there are two modes: 65 and 70 (bi-modal).
- Range: Highest − Lowest.
Range = 90 − 65 = 25.
6. Interpreting data — examples of questions
From the fruit survey above you can answer:
- Which fruit is most popular? Banana (12 pupils).
- Which fruit is least popular? Avocado (3 pupils).
- How many more pupils chose Banana than Apple? 12 − 6 = 6 pupils.
- What fraction of pupils chose Mango? 8/30 = 4/15. As a percentage ≈ 26.7%.
7. Practice (try these)
- A teacher records the number of books read by 8 pupils: 2, 5, 3, 4, 5, 2, 7, 4. Find the mean, median, mode and range.
- A survey of 20 pupils shows favourite sports: Football 8, Running 4, Volleyball 3, Hockey 5. Draw a pictogram with 1 symbol = 2 pupils.
- From the pictogram in section 3, what percentage chose Banana? (12 out of 30)
Answers (click to view)
1) Numbers: 2,5,3,4,5,2,7,4 → Sum = 32, mean = 32/8 = 4. Median (ordered 2,2,3,4,4,5,5,7) → middle = average of 4 and 4 = 4. Mode = 4 and 5? (both appear twice) → modes: 4 and 5. Range = 7 − 2 = 5.
2) Pictogram: Football: 8 → 🍏🍏🍏🍏 (4 symbols if 1 = 2 pupils), Running: 4 → 🍏🍏 (2 symbols), Volleyball: 3 → 🍏🍏 (1.5 symbols, show half if needed), Hockey: 5 → 🍏🍏🍏 (2.5 symbols). Explain halves clearly.
3) Percentage for Banana: 12/30 = 0.4 = 40%.
2) Pictogram: Football: 8 → 🍏🍏🍏🍏 (4 symbols if 1 = 2 pupils), Running: 4 → 🍏🍏 (2 symbols), Volleyball: 3 → 🍏🍏 (1.5 symbols, show half if needed), Hockey: 5 → 🍏🍏🍏 (2.5 symbols). Explain halves clearly.
3) Percentage for Banana: 12/30 = 0.4 = 40%.
8. Tips & summary
- Always check that totals match the number of people surveyed.
- Use tally marks when collecting to avoid mistakes.
- Choose the best chart: use bar graphs for comparisons, pictograms for simple class displays and line graphs for change over time (e.g. rainfall).
- Mean, median and mode give different information — use the one that answers your question.
Good luck! Practice by collecting simple data from your class, home or neighbourhood.