GRADE 8 Mathematics DATA HANDLING AND PROBABILITY β Data Presentation and Interpretation Notes
Data Handling and Probability β Data Presentation & Interpretation
Subject: Mathematics | Topic: DATA HANDLING AND PROBABILITY | Subtopic: Data Presentation and Interpretation | For Kenyan learners (age ~13)
What is "Data Presentation and Interpretation"?
Data presentation means showing numbers or information using tables, charts or pictures. Interpretation means reading those tables or charts to answer questions, find patterns, and make conclusions (for example: which group is biggest, what is the average, or whether numbers are increasing).
Types of Data
- Categorical (qualitative): names or groups (e.g., favourite sport: Football, Volleyball).
- Numerical (quantitative): numbers you can count or measure. - Discrete: whole numbers (number of pupils).
- Continuous: measured values (length, time).
- Numerical (quantitative): numbers you can count or measure. - Discrete: whole numbers (number of pupils).
- Continuous: measured values (length, time).
Common Ways to Present Data
- Tally and Frequency tables
- Bar charts and Pictograms
- Pie charts
- Histograms (for grouped numerical data)
- Stem-and-leaf and Dot plots (for small sets)
- Bar charts and Pictograms
- Pie charts
- Histograms (for grouped numerical data)
- Stem-and-leaf and Dot plots (for small sets)
1) Tally and Frequency Table
Use tally marks (||||) to count, then write the totals in the frequency column.
| Sport | Tally | Frequency |
|---|---|---|
| Football | |||| || | 7 |
| Volleyball | |||| | 4 |
| Athletics | |||| ||| | 8 |
| Basketball | || | 2 |
2) Bar Chart (Simple)
Bar charts are good for comparing categories. Example below uses the same sport frequencies.
Tip: Choose equal spaces and start the axis at zero to avoid misleading bars.
3) Pictogram
Use pictures to represent a number of units. One picture can stand for 1 person, or 2 persons etc. Always include a key.
Key: π = 2 students
Basketball: ππ
Here basketball frequency = 4 (because each ball = 2 students).
4) Pie Chart (Simple)
Pie charts show parts of a whole. Angles are found by: (frequency / total) Γ 360Β°.
5) Histogram (Grouped Data)
Use for continuous data grouped into equal class intervals. Bars touch each other. Example: Test scores grouped as 0β9, 10β19, 20β29, ... with frequencies.
| Score (marks) | Frequency |
|---|---|
| 0 β 9 | 1 |
| 10 β 19 | 3 |
| 20 β 29 | 5 |
| 30 β 39 | 1 |
Reading and Interpreting Data
When reading a chart:
- Check the title and labels (what are we measuring?).
- Check units (people, kg, marks).
- Look for highest/lowest, trends (increasing/decreasing), and totals.
- Be careful: some graphs start the axis at a number higher than zero which can mislead.
- Check units (people, kg, marks).
- Look for highest/lowest, trends (increasing/decreasing), and totals.
- Be careful: some graphs start the axis at a number higher than zero which can mislead.
Measures of Central Tendency (for interpretation)
For a list of numbers we often find:
- Mode: number that appears most.
- Median: middle number when data are ordered.
- Mean (average): add all values Γ· number of values.
- Range: highest β lowest.
- Median: middle number when data are ordered.
- Mean (average): add all values Γ· number of values.
- Range: highest β lowest.
Worked Example:
The marks of 7 pupils in a short test are: 6, 12, 15, 9, 12, 18, 10.
The marks of 7 pupils in a short test are: 6, 12, 15, 9, 12, 18, 10.
Step 1 β Order data: 6, 9, 10, 12, 12, 15, 18
Mode: 12 (appears twice)
Median: middle value (4th of 7) = 12
Mean: (6+12+15+9+12+18+10) = 82; 82 Γ· 7 β 11.71
Range: 18 β 6 = 12
How to Answer Interpretation Questions
- Read the question carefully β what is asked (total, difference, percentage, average)?
- Show working (e.g., how you calculated an angle for a pie chart).
- Give answers with correct units (students, kg, marks, %).
- Check if the chart needs scaling (e.g., 1 cm = 2 people).
- Show working (e.g., how you calculated an angle for a pie chart).
- Give answers with correct units (students, kg, marks, %).
- Check if the chart needs scaling (e.g., 1 cm = 2 people).
Example Question with Solution
Question: From the first frequency table (sports), how many pupils were asked in total? Which sport was most popular? What percentage chose Football? (Round to 1 decimal place.)
Solution: Total = 7 + 4 + 8 + 2 = 21 pupils.
Most popular = Athletics (8 pupils).
Percentage for Football = (7 Γ· 21) Γ 100% = 33.333...% β 33.3%.
Most popular = Athletics (8 pupils).
Percentage for Football = (7 Γ· 21) Γ 100% = 33.333...% β 33.3%.
Common Mistakes to Avoid
- Forgetting to use the key in a pictogram.
- Starting a bar chart vertical axis at a number > 0 without reason (this can mislead).
- Using pie charts for data that do not add to a meaningful whole.
- Mixing grouped and ungrouped data incorrectly when calculating median or mean.
- Starting a bar chart vertical axis at a number > 0 without reason (this can mislead).
- Using pie charts for data that do not add to a meaningful whole.
- Mixing grouped and ungrouped data incorrectly when calculating median or mean.
Practice Questions
1) A class of 20 students voted for their favourite fruit: Mango 6, Orange 5, Banana 4, Apple 5. Draw a suitable chart and find the mode.
2) The ages of 9 students: 12, 13, 12, 14, 13, 15, 13, 12, 14. Find mean, median and mode.
3) A pie chart shows clubs in school. If Soccer has angle 144Β° and total students in clubs are 90, how many students are in Soccer?
2) The ages of 9 students: 12, 13, 12, 14, 13, 15, 13, 12, 14. Find mean, median and mode.
3) A pie chart shows clubs in school. If Soccer has angle 144Β° and total students in clubs are 90, how many students are in Soccer?
Show Answers (click)
Answers:
1) Mode = Mango (6). You can draw a bar chart or pictogram (key).
2) Order: 12,12,12,13,13,13,14,14,15. Mean = (12+13+12+14+13+15+13+12+14)= 118 Γ· 9 β 13.11. Median = 13 (5th value). Mode = 12 and 13 (both appear 3 times) β bimodal.
3) Angle for Soccer = 144Β°. Fraction = 144/360 = 0.4. Students = 0.4 Γ 90 = 36 students.
1) Mode = Mango (6). You can draw a bar chart or pictogram (key).
2) Order: 12,12,12,13,13,13,14,14,15. Mean = (12+13+12+14+13+15+13+12+14)= 118 Γ· 9 β 13.11. Median = 13 (5th value). Mode = 12 and 13 (both appear 3 times) β bimodal.
3) Angle for Soccer = 144Β°. Fraction = 144/360 = 0.4. Students = 0.4 Γ 90 = 36 students.
Final Tips for Kenyan Learners (Age 13)
- Practice drawing neat tables and labelled chartsβexam markers look for clear labels and scales.
- Always write the units (e.g., pupils, %).
- Check arithmetic carefully when finding averages and percentages.
- Use a ruler for straight axes and equal spaces for bars.
- Always write the units (e.g., pupils, %).
- Check arithmetic carefully when finding averages and percentages.
- Use a ruler for straight axes and equal spaces for bars.
Good luck! Practise with data from your class (attendance, favourite food, homework time) β real data helps learning.