Page 110 - MAT KS3 Y8 Cambridge CheckPoint

10.3 Using statistics to compare two distributions

3 This table shows the goals scored by Juventus and AC Milan in each match in the Italian Premier
League in the 2010–11 season.
Goals scored 0 1 2 3 4 5 6 7

Number of Juventus 5 8 14 6 3 1 0 1
matches AC Milan 9 9 9 6 3 0 2 0

Compare the average number of goals per match scored by each team.
4 These are the heights of two groups of children, measured to the nearest centimetre.

Height (cm) 120–124 125–129 130–134 135–139 140–144 145–149
Boys 4 10 10 6 4 2
Girls 4 13 20 22 13 8
What is the difference between the average heights of the boys and the girls?
Give a reason for your answer.
5 This table shows the rainfall in a town in May and November, over a period of 25 years.

Rainfall (cm) 0– 5– 10– 15– 20– 25–
Number of May 7 11 4 2 1 0
years November 0 3 4 7 7 4

Compare the rainfall in May and November. Find any statistics that will be useful.
6 A group of people went on a special diet for three months. The table shows their masses before and
after the diet.

Mass (nearest kg) 80–84 85–89 90–94 95–99 100–104 105–109 110–114
Number of Before diet 0 0 5 6 8 12 14
people After diet 4 5 7 15 8 4 2

a How many people went on the diet?
b Did everyone lose mass? Give a reason for your answer.
c How did the range of masses change?
d What was the average reduction in mass? Give a reason for your answer.

Summary

You should now know that: You should be able to:
★ The mean, median and mode are averages and the ★ Calculate statistics for sets of discrete and
range is a measure of spread. continuous data.
★ The mean, median and range can be found from a ★ Recognise when to use the range, mean, median,
simple frequency table where the data is not mode and, for grouped data, the modal class.
grouped. ★ Compare two distributions, using the range and
★ The modal class in a grouped frequency table one or more of the mode, median and mean.
is the class with the largest frequency. ★ Record and compare reasoning, solutions and
★ The mean cannot be found exactly from a conclusions.
grouped frequency table but it can be estimated
by using the midpoint of each class.
★ You can use averages or ranges to compare two
distributions.

108 10 Processing and presenting data