Averages and Measures of Spread
9.3 Averages and Measures of Spread – Cheat Sheet
1. Mean, Median, Mode, Range (Individual Data)
| Measure | Formula / Method | Purpose | Notes |
|---|---|---|---|
| Mean | Mean = (Σx) / n | Shows overall average | Affected by extreme values |
| Median | Arrange data in order → middle value | Shows central tendency | Not much affected by extremes |
| Mode | Most frequent value | Shows most common value | Useful for categorical data |
| Range | Range = Maximum − Minimum | Measures spread | Affected by extreme values |
Example – Individual Data
Data: 4, 6, 8, 5, 7
- Mean = (4 + 6 + 8 + 5 + 7) / 5 = 30 / 5 = 6
- Median = 6 (middle value after ordering: 4, 5, 6, 7, 8)
- Mode = None (no repeated value)
- Range = 8 − 4 = 4
2. Estimated Mean for Grouped Data
| Class Interval | Frequency (f) | Midpoint (x) | f × x |
|---|---|---|---|
| 0–10 | 5 | 5 | 25 |
| 10–20 | 8 | 15 | 120 |
| 20–30 | 7 | 25 | 175 |
| Total | 20 | — | 320 |
Formula: Estimated mean = (Σf × x) / (Σf)
Calculation: Estimated mean = 320 / 20 = 16
3. Modal Class (Grouped Data)
- Modal class = class interval with the highest frequency
Example: In the table above, 10–20 has the highest frequency (8) → Modal class = 10–20
4. Purpose of Measures
| Measure | Best used for |
|---|---|
| Mean | Overall performance when no extreme values |
| Median | Data with outliers or skewed distribution |
| Mode | Most common category or value |
| Range | Quick idea of spread |