Two curves on one grid The curves show the marks of 80 students in Group A and 120 students in Group B in the same test. Read each curve at its own total: Group A at 20, 40, 60; Group B at 30, 60, 90. **Group** | **n** | **Q_1** | **Median** | **Q_3** | **IQR** A | 80 | 20 | 30 | 40 | 20 B | 120 | 30 | 40 | 55 | 25 Two comments A comparison needs two comments. Each names the statistic, gives both values and says what it means in the context. **Comment on** | **Statistic** | **Example** the average | median | On average Group B scored higher: its median, 40 marks, is greater than Group A’s, 30 marks. the spread | interquartile range | Group A’s marks are more consistent: its interquartile range, 20 marks, is smaller than Group B’s, 25 marks. Compare percentages, not heights At 40 marks both curves are at height 60, but that is 6080=75% of Group A and only 60120=50% of Group B. When the totals differ, change counts into percentages before comparing. When the totals are equal, the curve that is higher at a mark has more students at or below that mark, so that group generally scored lower. Checks and common errors - Read each curve at its own total. - A higher median is not automatically better: for waiting times or race times, lower is better. Say what the statistic means in the context. - Write both comments; one comment on the average alone does not compare spread.

Comparing two cumulative frequency curves

Secondary 4

Two curves on one grid

The curves show the marks of $80$ students in Group A and $120$ students in Group B in the same test. Read each curve at its own total: Group A at $20$, $40$, $60$; Group B at $30$, $60$, $90$.

Group	$n$	$Q_1$	Median	$Q_3$	IQR
A	$80$	$20$	$30$	$40$	$20$
B	$120$	$30$	$40$	$55$	$25$

Two comments

A comparison needs two comments. Each names the statistic, gives both values and says what it means in the context.

Comment on	Statistic	Example
the average	median	On average Group B scored higher: its median, $40$ marks, is greater than Group A’s, $30$ marks.
the spread	interquartile range	Group A’s marks are more consistent: its interquartile range, $20$ marks, is smaller than Group B’s, $25$ marks.

Compare percentages, not heights

At $40$ marks both curves are at height $60$, but that is $\dfrac{60}{80}=75\%$ of Group A and only $\dfrac{60}{120}=50\%$ of Group B. When the totals differ, change counts into percentages before comparing. When the totals are equal, the curve that is higher at a mark has more students at or below that mark, so that group generally scored lower.

Checks and common errors

Read each curve at its own total.
A higher median is not automatically better: for waiting times or race times, lower is better. Say what the statistic means in the context.
Write both comments; one comment on the average alone does not compare spread.

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Group	\(n\)	\(Q_1\)	Median	\(Q_3\)	IQR
A	\(80\)	\(20\)	\(30\)	\(40\)	\(20\)
B	\(120\)	\(30\)	\(40\)	\(55\)	\(25\)