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10.2 Using statistics

4 Belts are sold in different lengths. Length (cm) 32 34 36 38 40 42 44 46
This table shows the number of men’s belts
sold in a shop during one month. Frequency 6 16 28 41 17 18 10 13

Use an appropriate average to decide which size of belt the shop owner should
always try to keep in stock.

5 These are the annual salaries (to the nearest thousand 23 000 26 000 26 000 29 000 29 000
dollars) of each employee of a small company. 30 000 30 000 32 000 46 000 59 000
Work out the average annual salary for the company.

6 This table shows the lengths of 58 new movies.
Length (minutes) 80− 90− 100− 110− 120− 130− 140−150
Frequency 3 10 12 26 2 4 1

Work out the average length of a new movie.
7 These are the numbers of breakdowns on a motorway 2 5 8 6 4 9 6 3 6 4 7 4
on 12 different days in the summer.
These are the numbers for 10 days in the winter. 10 13 6 14 7 19 7 15 16 7
Compare the number of breakdowns in summer and
winter. Calculate any statistics you need.

8 Three runners each take part in a number of
half marathons in one year. Here are their Andi 91 83 90 86 88 88
times, to the nearest minute. Bart 90 96 96 77 99 78 88 95
a Who is the fastest runner?
b Who is the most consistent runner? Chris 89 91 92 92 91
Find statistics to support your answers.
9 Here are the lengths of text messages that Obi and Darth sent during one month from their mobiles.

Characters 1−20 21−40 41−60 61−80 81−100 101−120
Obi 6 32 51 27 11 7

Darth 21 42 16 5 0 0
Compare Obi’s and Darth’s phone use. Work out any statistics you need.

Summary

You should now know that: You should be able to:
+ The mean, the median and the mode are three + Calculate statistics, including the mean, the
different types of average. median, the mode and the range.

+ The range is a statistic that measures the spread + Select the most appropriate statistics for a
of a set of data. particular problem.
+ The average is a representative value and you + Decide how to check results by considering
can use this fact to check for possible errors in whether the answer is reasonable in the context of
calculation. the problem.

10 Processing and presenting data 101