Statistics Foundation · Lesson 2.2
Measures of spread.
Measures of spread describe how variable, consistent or dispersed the data are. This lesson teaches students how to interpret range, interquartile range, variance and standard deviation, why deviations from the mean matter, and how to choose a spread measure that matches the centre and shape of the data.
100–105 minute lesson plan
Learn how to describe consistency, variation and uncertainty in a dataset.
In Lesson 2.1, you learned how to describe the centre of a dataset. This lesson adds the second essential question: how spread out are the values? A centre without spread is incomplete because it hides consistency, inequality and risk.
0–10 min
Why spread matters
Understand why centre alone is not enough. Two datasets can have the same mean but very different levels of variability.
10–25 min
Range and interquartile range
Learn how the range captures the full distance from smallest to largest value, while the IQR focuses on the middle 50% of the data.
25–45 min
Deviations from the mean
Study how each value differs from the mean, and why deviations are the foundation of variance and standard deviation.
45–65 min
Variance and standard deviation
Learn why squared deviations are averaged, why the sample variance divides by n - 1, and why standard deviation returns to the original units.
65–85 min
Interactive spread lab
Adjust outliers, clustering and sample size to see how range, IQR, variance and standard deviation respond.
85–105 min
Worked examples and interpretation
Practise choosing and interpreting measures of spread for exam scores, waiting times, salaries and health measurements.
Mastery checklist
By the end, spread should feel like a story about variability.
Explain why centre alone is incomplete.
Calculate and interpret the range.
Explain quartiles and calculate the interquartile range.
Describe deviations from the mean.
Explain why variance uses squared deviations.
Interpret standard deviation in original units.
Choose between range, IQR and standard deviation.
Match spread summaries to data shape and outliers.