GCSE Statistics · Higher · Chapter 7: Spread, shape and comparing distributions · Lesson 1

Range, quartiles and interquartile range

About 50 minutesCalculator allowed38 marks

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The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
A final mark is worked out from the practical, worth 60%, and the written paper, worth 40%. Ella scored $77$ in the practical. What mark does Ella need in the written paper to get a final mark of $65$ ?
[2 marks]
Answer
A2
From chapter 2
Femi wants to know how the adults in a city travel to work. Femi asks people at the main train station at 8 am on a weekday. Give two reasons why the sample may not be representative.
[2 marks]
A3
From chapter 3
Noor's hypothesis is "More girls than boys choose tea as their favourite hot drink." The data collection sheet has rows Tea, Coffee, Hot chocolate, Other and columns Tally and Frequency. Is the sheet appropriate? Give a reason.
[2 marks]
A4
From chapter 3
Femi records four students' spelling test marks out of 40 before and after a month of using a spelling app. Before: 14, 32, 22, 14. After, in the same order: 10, 26, 20, 16. Work out the mean change from before to after.
[2 marks]
Answer

Your teacher works through each example with you. Then try the one beside it.

Example 1

Here are the numbers of emails received by 11 office workers one morning.

14, 9, 22, 17, 6, 31, 12, 19, 8, 25, 15

Work out the range and the interquartile range.

Hint Put the values in order. With

n

values the lower quartile is the

\frac{n + 1}{4}

th value.

Example 2

The table shows the numbers of goals a hockey team scored in 23 matches. Find the median and the interquartile range.

Hint Add a running total down the table. With 23 values the quartiles are the 6th and 18th values.

B2
The table shows the numbers of books borrowed by 39 library members in a month. Work out the interquartile range.
[3 marks]
Answer

Example 3

The cumulative frequency graph shows the times taken by 80 runners in a 5 km race. Work out an estimate of the interdecile range of the times.

Hint The interdecile range runs from the 10th percentile to the 90th. Read across at

10%

and

90%

of 80, not at 10 and 90.

B3
The cumulative frequency graph shows the distances travelled to work by 120 workers. Work out an estimate of the range between the 20th and the 80th percentiles of the distances.
[3 marks]
Answer

Example 4

Here are the numbers of minutes that 9 buses were late on Monday.

2, 0, 5, 3, 41, 1, 4, 6, 3

Give a reason why the interquartile range is a better measure of spread than the range for these times.

Hint Look for a value that is very different from the others, and ask which measure uses it.

B4
Here are the prices, in £, of 9 bikes in a shop.
240, 310, 275, 1890, 260, 295, 330, 285, 250
Explain why the interquartile range is a more suitable measure of spread than the range for these prices.
[2 marks]

C1
Here are the numbers of cars passing a school gate in eleven 10-minute periods, in order.
12, 15, 17, 20, 21, 24, 26, 29, $a$ , 35, 40
The interquartile range is 15. Find $a$ .
[2 marks]
Answer
C2
The interquartile range of the times that Year 10 students took to run 400 m is 18 seconds. Explain what this tells you about the times.
[1 mark]

C3
The stem-and-leaf diagram shows the ages of the 19 members of a choir. The 10th percentile is the $\frac{n + 1}{10}$ th value. Work out the interquartile range and the interdecile range of the ages.
[3 marks]
AnswerIQR $\dots\dots$ Interdecile $\dots\dots$
C4
A table groups the masses of 200 parcels into classes $0 < m \leq 1$ , $1 < m \leq 2$ , and so on up to $5 < m \leq 6$ kg. Explain why the range of the masses cannot be found from the table.
[1 mark]

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can find the range, quartiles and interquartile range from a list, a table or a stem-and-leaf diagram.
I can estimate interdecile and interpercentile ranges from a cumulative frequency graph.
I can explain why the interquartile range is not affected by extreme values.

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