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.
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 from raw data
Apply the core method for Mean (Average) in this section context.
Step by step
- Write the relevant formula or rule first to secure method marks.
- Substitute values from the question carefully and keep units/labels clear.
- Simplify and check whether the result is reasonable in context.
Final answer
Final answer should be clearly stated and interpreted for Mean (Average).
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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: Class [0-10): midpoint 5, frequency 4 Class [10-20): midpoint 15, frequency 6 Class [20-30): midpoint 25, frequency 5__LINEBREAK__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