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10.1 Calculating statistics

4 Find the mean age for each group in question 2.
5 Find the range of the ages for each group in question 2.
6 This table shows the daily pay for a group of workers. For grouped data,
the modal class is the
Pay (dollars) 40–59 60–79 80–99 100–119 class with the highest

Frequency 15 58 27 22 frequency. Also the range
is an estimate because
a What is the modal class? the table does not list
b Why can you not find the exact value for the mean pay? the exact values.

c Xavier is trying to find the range of the data.
Is he correct? Give a reason for your answer.
The range is 53 dollars.

7 Oditi records the midday temperature (to the nearest degree) in the school field every day for

one month.
Temperature (°C) −10 to −6 −5 to −1 0 to 4 5 to 9

Frequency 3 8 16 4
a What can you say about the median temperature?
b Estimate the range.
8 Ahmad has three test marks.
The lowest mark is 52.
The range is 37 marks.
The mean is 66.
What are the three marks?

9 These are the ages of a family of four children and their mother. 3, 5, 8, 12, 39
Work out:
a the mean age of the children
b the median age of the children.
If the age of the mother is included, what effect does this have on:
c the mean age d the median age?
10 Here are some statistics about the masses of a group of 40 children.

Mean = 12.5 kg Median = 11.7 kg Range = 6.1 kg

a If the mass of every child increases by 1.4 kg, what are the new statistics?
b If the mass of every child doubles, what are the new statistics?
11 Here is some data about a group of boys and a group of girls.
Boys: number: 20 mean height: 1.55 m range of heights: 0.42 m

Girls: number: 10 mean height: 1.40 m range of heights: 0.36 m

For the combined group of boys and girls, work out, if possible:
a the number of children b the mean height c the range of heights.

10 Processing and presenting data 99