Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown.
Level 1 · Warm-up
1 A distribution has its tail stretching to the right. Is it positively or negatively skewed?
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Positively skewed.
2 What is a value clearly separated from the rest of the data called?
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An outlier.
3 Which average is more affected by an outlier — the mean or the median?
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The mean.
Level 2 · Core
4 Find the mean of 12, 14, 15, 15, 16, 17, 48. (1 decimal place)
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19.6.
5 Find the median of 12, 14, 15, 15, 16, 17, 48.
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15.
6 Remove the 48. What is the new median of 12, 14, 15, 15, 16, 17?
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15 — unchanged, which is why the median is preferred with outliers.
Level 3 · Challenge
7 Most students score high on an easy test, with a few low scores. What shape is the distribution?
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Negatively skewed — the tail runs to the left.
8 A height is recorded as 1750 cm. Should you keep it or remove it?
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Remove it — it is an error, almost certainly 175.0 cm. Say why you removed it.
9 Name the four things a full description of a distribution must include.
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Centre, spread, shape and outliers — all in context.