This worksheet teaches students to find a dataset's five-number summary and interquartile range, identify outliers, and compare the centre, spread and shape of two distributions using boxplots. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- The five-number summary of a dataset is: minimum, lower quartile (Q1), median, upper quartile (Q3), maximum — this is what a boxplot displays.
- The interquartile range (iqr = Q3−Q1) measures the spread of the middle 50% of the data, and is less affected by outliers than the full range.
- The 1.5×iqr rule: a value is a statistical outlier if it lies below Q1−1.5×iqr, or above Q3+1.5×iqr.
- Comparing two boxplots: compare their centre (median), spread (iqr/range) and shape (symmetric, or skewed toward one side).
- A distribution is skewed when its mean and median differ noticeably, or when one "whisker"/side of the box is much longer than the other.
What your child will practise:
- Finding the five-number summary of a dataset (using the median-of-halves method for quartiles).
- Calculating the iqr and use the 1.5×iqr rule to identify outliers.
- Comparing the median (centre) of two datasets.
- Comparing the iqr or range (spread/consistency) of two datasets.
- Using mean vs median, or the position of the median within the iqr, to comment on a distribution's shape/skew.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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