Page 109 - MAT KS3 Y8 Cambridge CheckPoint

10.3 Using statistics to compare two distributions

10.3 Using statistics to compare two distributions

Suppose you have two sets of test marks, or the heights of two
The average that is most appropriate will
groups of people. How can you compare the two sets?
depend on the actual data.
One way is to find one or more of the averages, and the range.
The range will show which of the two sets of data is more spread out.

Worked example 10.3

These frequency tables show the masses of a group of girls and a group of boys.
Girls’ masses (kg) 16–20 21–25 26–30 31–35 36–40 41–45
Frequency 12 14 20 30 17 7

Boys’ masses (kg) 16–20 21–25 26–30 31–35 36–40 41–45 46–50
Frequency 5 18 15 18 29 11 14
Calculate suitable statistics to complare the two distributions.

The median for the girls is 31 kg. This was calculated in Worked example 10.2.
The median for the boys is 35 kg. There are 110 boys. The median is between the 55th
and 56th values. The table shows that 56 boys have a
mass of 35.5 kg or less.
The mean for the girls is 30.4 kg. This was calculated in Worked example 10.2.
The mean for the boys is 34.2 kg. Using the midpoints of the classes gives
3765 ÷ 110 = 34.2.
The median and the mean both show that on
average the mass of a girl is about 4 kg less
than the mass of a boy.
The range for the girls is between 20 and 30 kg. This was calculated in Worked Example 10.2.
The range for the boys is between 25 and 35 kg. This is larger because of the 46–50 kg group.
The range of the boys’ masses is estimated to be
about 5 kg more than the girls’ masses.

✦ Exercise 10.3 Paper 1 Paper 2

1 These are students’ marks in two test papers. Number of questions 20 15
a Which paper was more difficult? Marks available 100 100
b Which paper had a greater variation in marks? Median 46 41
Give reasons for your answers.
Mean 49.5 42.8
Range 38 27
Lowest mark 20 26

2 The users of two websites were asked to grade them for ease-of-use. They used a scale of 1 to 5.
1 was poor and 5 was excellent. The results are shown in this table.

Grade 1 2 3 4 5
Website A 4 10 16 20 10
Frequency
Website B 20 35 15 10 20

Use averages to decide which website is better.
10 Processing and presenting data 107