Statistics: Class 9 Study Guide
Statistics is the study of collecting, organising and understanding data.
Data collected first-hand is primary data, and data taken from a book or website is secondary data. Raw data is organised into a frequency table. For a large range of values, we group them into class intervals such as 0–10, 10–20 and 20–30.
A bar graph suits separate categories. A histogram suits grouped data, with touching bars whose widths show the class intervals. A frequency polygon joins the mid-points of the tops of the bars.
Measures of central tendency
The mean is the sum of the values divided by their number. The median is the middle value when they are in order, or the average of the two middle values if there are two. The mode is the value that occurs most often.
| Data: 4, 6, 8, 8, 9, 10, 11 | Value |
|---|---|
| Mean | (4 + 6 + 8 + 8 + 9 + 10 + 11) ÷ 7 = 56 ÷ 7 = 8 |
| Median | The 4th value, 8 |
| Mode | 8, which occurs twice |
Mean from a frequency table
Multiply each value by its frequency, add the products and divide by the total frequency. For the values 2, 3 and 4 with frequencies 3, 5 and 2: sum = 2×3 + 3×5 + 4×2 = 6 + 15 + 8 = 29, total frequency = 10, so the mean is 2.9.
Value and frequency.
Value × frequency.
Find both totals.
Total products ÷ total frequency.
Choosing a measure
The mean uses all values but is pulled by very large or small ones. The median is better when a few values are extreme, as with house prices. The mode suits the most common category, such as the most popular shoe size.
Worked examples and common mistakes
Example: Data 3, 5, 7, 9: the median is (5 + 7) ÷ 2 = 6. Common mistakes: finding the median without putting the data in order, using unequal bar widths in a histogram and leaving gaps between bars, and dividing by the number of classes instead of the total frequency.
Check your understanding: model answers
1. In order: 2, 4, 5, 7, 9, so the median is 5. 2. 52 ÷ 4 = 13. 3. A histogram.
✨ Key Takeaways
- Mean = sum ÷ number of values.
- Median is the middle value of ordered data.
- Mode is the most frequent value.
- A histogram has touching bars for grouped data.
💬 Questions for Discussion & Reflection
- Find the median of 2, 9, 4, 7, 5.
- Find the mean of 10, 12, 14 and 16.
- Which graph suits grouped data: bar graph or histogram?