Curriculum
Statistics — Third Secondary
Unit 1: Correlation and Regression
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Unit 2: Advanced Statistical Measures
0/2
Unit 3: Probability
0/2
Unit 4: Random Variables
0/4
Unit 5: The Normal Distribution
0/2
Text lesson
Advanced Measures of Dispersion
Advanced Measures of Dispersion
Standard deviation of grouped data
Standard deviation of grouped data
- In a frequency table, the class midpoints are used in place of the values.
- The midpoint of a class = (lower limit + upper limit) ÷ 2.
- The formulas are:
- x̄ = Σ(f × x) ÷ Σf, and σ² = Σ(f × (x − x̄)²) ÷ Σf
- where x is the class midpoint and f is the frequency of that class.
- The shortcut σ² = Σ(f × x²) ÷ Σf − (x̄)² can be used as a check.
| Class | Midpoint x | Frequency f |
|---|---|---|
| 10 to less than 20 | 15 | 3 |
| 20 to less than 30 | 25 | 5 |
| 30 to less than 40 | 35 | 8 |
| 40 to less than 50 | 45 | 4 |
Advanced Measures of Dispersion · 2 / 7