Range definition
Big Idea: Range = highest value - lowest value.
Simplest measure of spread.
Tells you how wide the data is but ignores values in between.
Limitation: Range is very sensitive to outliers.
One extreme value can make range huge.
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Standard deviation
Big Idea: Standard deviation (s or σ) measures how far data points typically deviate from the mean.
Larger SD = more spread.
Small SD = data clustered near mean.
Worked example - Standard deviation
Apply the core method for Range and Standard Deviation 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 Range and Standard Deviation.
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Variance
Variance = SD²: Variance is standard deviation squared.
Both measure spread, but SD is easier to interpret (same units as data).
Variance is used in formulas.
Worked example - Variance
Apply the core method for Range and Standard Deviation 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 Range and Standard Deviation.
When to compare spreads
Compare using SD: Use SD when comparing spread of two datasets (e.g., which class has more consistent exam scores?).
SD and Range together tell full picture: range shows extremes, SD shows typical deviation.
Interpretation: SD ≈ 1/3 of range is a rough rule of thumb for normal data.