This worksheet teaches students to compare multiple data distributions using centre, spread and shape, and calculate how an outlier affects the mean far more than the median. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- Centre is measured by the mean (average) or median (middle value); spread is measured by the range (max−min) or the interquartile range, iqr=Q3−Q1.
- The quartiles Q1 and Q3 are the medians of the lower and upper halves of an ordered dataset (excluding the overall median if the dataset size is odd).
- The standard rule for identifying an outlier: any value below Q1−1.5×iqr or above Q3+1.5×iqr.
- The mean is heavily affected by an outlier (it's pulled toward the extreme value); the median is far more resistant, since it only depends on the middle position(s), not the actual extreme value.
- Two datasets can have the same mean but very different medians, ranges and shapes — mean alone doesn't tell the full story of a distribution.
What your child will practise:
- Calculating the mean, median and range of a dataset.
- Calculating Q1, Q3 and the interquartile range (iqr) of a dataset.
- Applying the 1.5×iqr rule to identify outliers.
- Quantifying how much an outlier shifts the mean compared to the median, by comparing statistics with and without it.
- Comparing two datasets' centre, spread and shape, and explain what the comparison reveals (or conceals) about each.
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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