CAIE IGCSE Mathematics Extended 9 Statistics Topic Practice

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Covered syllabus points

E9.1 Classifying statistical dataE9.2 Interpreting statistical dataE9.3 Averages and measures of spreadE9.4 Statistical charts and diagramsE9.5 Scatter diagramsE9.6 Cumulative frequency diagramsE9.7 Histograms

Question 1

[Maximum number: 4]

These are Rahul's 10 test scores.
9
8
9
10
7
x
9
9
x
7

The mean of these scores is 8.

Find the interquartile range.
You must show all your working.

Question 2

[Maximum number: 12]

Question (a)

(a)

Jean asks 600 people to choose their favourite sport. The pie chart shows some of this information.

Figure for Question (a) — CAIE IGCSE Mathematics Extended
[ 5 ]

Question (i)

(i)

Show that 100 people choose tennis.

[ 1 ]

Question (ii)

(ii)

Work out how many people choose rugby.

[ 2 ]

Question (iii)

(iii)

125 people choose cricket and the rest choose swimming.

Complete the pie chart to show this information.

[ 2 ]

Question (b)

(b)

The heights of some plants are measured:
- smallest height =0.6 cm=0.6 \mathrm{~cm}
- range =8.1 cm=8.1 \mathrm{~cm}
- median =5.2 cm=5.2 \mathrm{~cm}
- lower quartile =3.4 cm=3.4 \mathrm{~cm}
- interquartile range =4.1 cm=4.1 \mathrm{~cm}.

On the grid, draw a box-and-whisker plot to show this information.

Figure for Question (b) — CAIE IGCSE Mathematics Extended
[ 3 ]

Question (c)

(c)
Table for Question (c) — CAIE IGCSE Mathematics Extended

50 students answer a mathematics question.

The table shows the time, t seconds, taken by each student to answer the question.

\begin{tabular}{|l||c|c|c|c|c|}
\hline Time (t seconds) & 10<t⩽2010<t\leqslant20 & 20<t⩽2520<t\leqslant25 & 25<t⩽3025<t\leqslant30 & 30<t⩽5030<t\leqslant50 & 50<t⩽8050<t\leqslant80 \\
\hline Frequency & 2 & 8 & 12 & 16 & 12 \\
\hline
\end{tabular}

Calculate an estimate of the mean.

[ 4 ]

Question 3

[Maximum number: 10]

A student measures the height, h cmh \mathrm{~cm}, of each of 400 plants.

Question (a)

(a)

The cumulative frequency diagram shows the results.

Figure for Question (a) — CAIE IGCSE Mathematics Extended

Use the diagram to find an estimate for

[ 7 ]

Question (i)

(i)

the median cm [1]

[ 1 ]

Question (ii)

(ii)

the interquartile range cm [2]

[ 2 ]

Question (iii)

(iii)

the 80th percentile cm [2]

[ 2 ]

Question (iv)

(iv)

the number of plants with a height greater than 60 cm .

[ 2 ]

Question (b)

(b)

The heights are also shown in the frequency table.

Table for Question (b) — CAIE IGCSE Mathematics Extended

Complete the histogram to show this information.

Figure for Question (b) — CAIE IGCSE Mathematics Extended
[ 3 ]

Question 4

[Maximum number: 5]

Students in class P take a test.
These statistics show information about their marks.
- lower quartile =38
- median =53
- interquartile range =28
- range =81
- highest mark =96

Question (a)

(a)

Draw a box-and-whisker plot to represent this information.

Figure for Question (a) — CAIE IGCSE Mathematics Extended
[ 3 ]

Question (b)

(b)

Students in class Q take the same test.

For class Q, the median is 49 and the interquartile range is 35.
Make two comments comparing the distribution of marks for class P with that of class Q.
1.
2.

[ 2 ]
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