Data handling Notes, Quizzes & Revision
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Mathematics β DATA HANDLING
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.
| Fruit | Tally | Frequency |
|---|---|---|
| Banana | |||| |||| || | 12 |
| Mango | |||| |||| | 8 |
| Apple | |||| | | 6 |
| Avocado | ||| | 3 |
| Total | 30 |
(Each π = 2 pupils)
Mango: ππππ (=8) (used π for mango)
Apple: πππ (=6)
Avocado: π₯π₯ (β3 shown as 1.5βexplain 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).
- 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 Γ· 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 β middle (4th) = 70. Median = 70.
- Mode (most frequent): The score that appears most often.
65 appears twice, 70 appears twice β there are two modes: 65 and 70 (bi-modal).
- Range: Highest β Lowest.
Range = 90 β 65 = 25.
6. Interpreting data β 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 β 6 = 6 pupils.
- What fraction of pupils chose Mango? 8/30 = 4/15. As a percentage β 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)
2) Pictogram: Football: 8 β ππππ (4 symbols if 1 = 2 pupils), Running: 4 β ππ (2 symbols), Volleyball: 3 β ππ (1.5 symbols, show half if needed), Hockey: 5 β πππ (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 β use the one that answers your question.