Revision GuideStatistics & Data
Statistics Revision Guide
A fuller printable guide to descriptive statistics, centre measures, spread measures, and interpretation habits that help prevent misleading summaries.
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Quick Reference SheetStatistics & Data
Measures of Spread Quick Reference
A stronger spread reference sheet for variance, standard deviation, range, and z-scores, with interpretation guidance.
Filename: measures-of-spread-quick-reference.pdfFile size: 3 KB
Formula highlights
Variance
sigma^2 = sum((x - mean)^2) / N
Standard deviation
sigma = sqrt(variance)
What spread tells you
Spread measures how widely the data are dispersed around a centre. It complements, rather than replaces, measures such as the mean or median.
Core relationships
- Range = maximum - minimum
- Variance averages squared deviations in the chosen model
- Standard deviation is the square root of variance
- Z-score standardises a value relative to the mean and standard deviation
Interpretation reminders
- Range is quick but sensitive to extremes.
- Standard deviation is often easier to interpret than variance because it returns to the original units.
- A z-score shows how unusual a value is relative to the distribution model.
Worked examples
Use range for a fast first look, then standard deviation when you need a fuller picture of spread.
A high positive z-score suggests a value well above the mean, while a negative z-score indicates a value below it.
Related calculators
Use the formulas in live tools.
Range Calculator
Use the Range Calculator to calculate range from your own dataset with practical output and sensible validation.
Statistics & DataOpen
Variance Calculator
Use the Variance Calculator to calculate variance from your own dataset with practical output and sensible validation.
Statistics & DataOpen
Standard Deviation Calculator
Measure how widely a dataset spreads around its average by calculating the standard deviation.
Statistics & DataOpen
Z-Score Calculator
Calculate how far a value sits from the dataset mean in standard-deviation units.
Statistics & DataOpen
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