Definition and formula
Big Idea: The mean is the average—add all values and divide by how many values.
Use the mean when the data is roughly symmetric and you want to include all values.
IB context: IB uses mean and average interchangeably.
Always check whether all values are included or if there are outliers.
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Mean from raw data
Raw data example: Data: 5, 7, 3, 8, 9, 5 Sum = 5 + 7 + 3 + 8 + 9 + 5 = 37 Count = 6 Mean = 37 ÷ 6 ≈ 6.17
| Data set | Calculation | Mean |
|---|---|---|
| 2, 4, 6, 8 | (2+4+6+8)÷4 | 5 |
| 10, 10, 10, 10 | (10+10+10+10)÷4 | 10 |
| 1, 1, 100 | (1+1+100)÷3 | 34 |
Worked example — mean of test scores
Eight students scored: 72, 85, 68, 91, 77, 84, 80, 75.
Find the mean.
Step by step
- Add all the values.
- Divide by the number of values.
- Check the answer is reasonable: 79 sits in the middle of the data range (68 to 91).
Final answer
Mean = 79.
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Mean from grouped data
The method: For frequency tables: multiply each class midpoint by its frequency, sum all products, then divide by total frequency.
Worked example — mean from grouped data
A frequency table shows the grouped data below.
| Class | [0-10) | [10-20) | [20-30) |
|---|---|---|---|
| Midpoint | 5 | 15 | 25 |
| Frequency | 4 | 6 | 5 |
Calculate the mean.
Solution
- Set up a calculation table: (midpoint) × (frequency)
- Sum all products: 20 + 90 + 125
- Find total frequency: 4 + 6 + 5 = 15
- Calculate mean: 235 ÷ 15
Final answer
Mean ≈ 15.67 (lies in the [10-20) class, as expected)
Key limitation: We lose information by grouping: we assume all values in a class are at the midpoint.
This introduces estimation error—the true mean might differ slightly.
In exam: Show the calculation table clearly, then state the formula and substitute values step by step.
When to use mean
Use mean when: Data is roughly symmetric You want one representative value No extreme outliers Values are quantitative (measurements, not categories)
Caution: Dont use mean if outliers are present Mean can be misleading for skewed data Compare with median to check for skew