Page 111 - Mathematics Coursebook

10.3 Comparing distributions

4 Nils recorded the temperatures in two experiments.

First experiment (°C) 29, 28, 21, 33, 30
Second experiment (°C) 28, 29, 28, 33, 32, 31, 32, 29

a Work out the mean, the median and the range for each experiment.
b State whether each of these statements is TRUE or FALSE.
i The temperatures in the first experiment are higher, on average, than the temperatures in the
second experiment.
ii The temperatures in the first experiment are more varied that the temperatures in the second
experiment.
c Can you work out the modal temperature for each experiment? Explain your answer.
5 A nurse measured the total mass of 20 baby boys as 64 kg. The total mass of 15 baby girls was 51 kg.
Which were heavier, the boys or girls? Give a reason for your answer.
6 In a large town there are three sports clubs. Here is some information about the ages of the people
who belong to each club.

Age of youngest
Club Number of people Mean age (years) Age range (years)
person (years)
Football 46 24 23 9
Swimming 32 29 32 7

Athletics 23 18 11 12

Use the information in the table to answer these questions. Give reasons for your answers.
a Work out the age of the oldest person in each club.
b Which club has the highest average age?
c Which club has the greatest variation in ages?

Summary

You should now know that: You should be able to:
+ Mode, median and mean are three types + Find the mode, median and range for a set of
of average. numbers or values.
+ The mode is the most common value. + Find the modal class for a set of grouped data.
+ The modal class is the class with the + Calculate the mean of a set of numbers.
highest frequency. + Calculate the mean from a simple frequency table.
+ The median is the middle value when a set of + Compare two simple distributions, using the
values is listed in order. range and the mode, median or mean.
+ To find the mean you add all the values and divide + Work logically and draw simple conclusions.
by the number of values.

+ The range is the difference between the
largest value and the smallest value. It
measures variation.

110 10 Averages