SM3.3 Statistics of grouped data
You can find the mean, median and mode of data given in class intervals, and say which of the three answers a given question honestly.
Topics shown in module order.
Real data arrives in groups: so many students in this mark range, so many in the next. The chapter adapts the three averages to that shape, the mean through midpoints of intervals, the median by walking the cumulative counts to the middle, the mode from the tallest interval and its neighbours. The quieter lesson is that the three can disagree, and which one to trust depends on what is being asked.
Work through these
Find the mean of a grouped table using midpoints, laying the working out in columns
The column layout, intervals, midpoints, frequencies, products, is the method. It is also the layout examiners award steps for, so practising it as a table rather than a scramble pays twice.
Build the cumulative frequency column and use it to find the median class and the median
The cumulative column is a running total, and the median class is where the halfway count falls. Seeing the formula as walking to the middle of the data, rather than as symbols, is what makes it rememberable.
Find the mode from the modal class formula, and check it lands inside the modal class
The formula sharpens the tallest bar of a histogram to a point, and the point must lie inside that bar. The check takes seconds and catches nearly every substitution error this formula invites.
For three described situations, say whether mean, median or mode answers the question, and why
A typical income, a fair average mark, the most common shoe size: each wants a different one of the three. This judgement is the part of statistics that stays useful after the formulas fade.
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Links last checked 7 Sept 2026.
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