Data Handling: Pie Charts, Histograms and Probability: Class 8 Study Guide
Data in a good chart tells its story at a glance. Probability tells us what to expect from chance.
Large sets of data are grouped into class intervals (for example 0–10, 10–20) in a frequency table. A histogram shows the frequency of each class with touching bars; there are no gaps because the data is continuous. A pie chart shows how a whole is divided: each sector's angle = (value ÷ total) × 360°.
Probability of an event = number of favourable outcomes ÷ total number of equally likely outcomes. It lies between 0 and 1. The probabilities of all outcomes of an experiment add to 1, so P(not E) = 1 − P(E).
Making a pie chart
Suppose 40 students choose a sport: cricket 16, football 12, hockey 8 and badminton 4. Angles: cricket 16/40 × 360 = 144°, football 108°, hockey 72° and badminton 36°. They add to 360°. Label each sector with the name and the percentage.
| Sport | Students | Angle |
|---|---|---|
| Cricket | 16 | 144° |
| Football | 12 | 108° |
| Hockey | 8 | 72° |
| Badminton | 4 | 36° |
Histograms
Class intervals must be of equal width for simple histograms, with the horizontal axis showing marks and the vertical axis the frequency. Tall bars show where most values lie. Compare it with a bar graph: in a bar graph the bars are separate and categories are discrete.
For example 10 marks wide.
Count each class.
Height = frequency.
State what is measured.
Probability
A die is rolled. P(prime number) = 3/6 = 1/2 (2, 3, 5). P(number greater than 4) = 2/6 = 1/3. A bag has 5 red, 3 green and 2 blue balls: P(green) = 3/10 and P(not blue) = 8/10 = 4/5. Experiments show that the relative frequency gets closer to the theoretical probability as the number of trials grows. A probability cannot be negative or greater than 1.
Worked examples and common mistakes
Example: Two coins are tossed. The outcomes are HH, HT, TH, TT, so P(exactly one head) = 2/4 = 1/2. Common mistakes: leaving gaps in a histogram, computing pie angles from the percentage without multiplying by 3.6 and counting outcomes that are not equally likely. List the sample space first.
Check your understanding: model answers
1. 90°. 2. 3/6 = 1/2. 3. 0.7.
✨ Key Takeaways
- Pie angle = value ÷ total × 360°.
- Histogram bars touch.
- P(E) is between 0 and 1.
- P(not E) = 1 − P(E).
💬 Questions for Discussion & Reflection
- Find the pie chart angle for 25 out of 100.
- Find P(even number) when a die is rolled.
- If P(rain) = 0.3, what is P(no rain)?
Print graph paper for charts →