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Australia
Year 8

10.05 Outliers

Worksheet
Outliers
1

Identify the outlier in the following data sets:

a

5, \,6, \,7, \,8, \,9, \,9, \,18

b

59, \,61, \,63, \,70, \,73, \,76, \,113

c

10, \,7, \,6, \,8, \,1, \,10, \,6

d

73, \,65, \,72, \,68, \,74, \,57, \,121

2

Identify the outlier(s) in the following data sets:

a

The marks achieved by students in a class on a particular math exam were:

66, \,74, \,62, \,64, \,60, \,24, \,68, \,67, \,70, \,61, \,58, \,57, \,73, \,71, \,75, \,63
b

Rochelle recorded the heights (in centimetres) of all the students in her class:

148, \,153, \,137, \,142, \,140, \,146, \,136, \,143, \,135, \,144, \,189, \,138, \,149, \,139, \,145, \,150

c

Frank has just finished a successful cricket season. Over the course of the season, he managed to make the following number of runs in each of his innings:

50, \,53, \,54, \,8, \,51, \,46, \,48, \,61, \,56, \,49, \,55, \,59, \,44, \,104

3

The following graphs show the annual net profit (in millions) of a company over a several year period. For each graph, state the year in which the annual net profit is an outlier:

a
b
4

For each of the following sets of data identify the outlier(s):

a
Hours per week
11
26\ 7\ 9
31\ 2\ 2\ 4\ 4\ 5\ 6\ 7\ 8\ 9
41

Key: 5\vert 2 = 52 hours

b
Leaf
23
3
4
5
6
71\ 3\ 5\ 8
81\ 3\ 3\ 4\ 5
93\ 4

Key: 1|2=12

c
d
Effects of outliers
5

For each of the following sets of data:

i

Find the mean, median, mode, and range. Round your answers to two decimal places where necessary.

ii

Identify the outlier.

iii

Remove the outlier from the set and recalculate the values found in part (i).

iv

Describe how each of the four statistics changed after removing the outlier.

a
53, \, 46,\, 25,\, 50,\, 30,\, 30,\, 40,\, 30,\, 47,\, 109
b
27, \,50, \,24, \,37, \,47, \,41, \,27, \,126, \,44, \,27
c
4.7,\, 2.8,\, 1.9,\, 0.9,\, 0.9,\, 2.2,\, 2.2,\, 1.2,\, 1.5,\, 0.9
d
4700,\, 4700,\, 4700,\, 4500,\, 5300,\, 4900,\, 5200,\, 4800,\, 1500,\, 5100
6

When an outlier is removed from a data set, describe the effect on the following:

a
Mode
b
Range
c
Mean
d
Median
7

Consider this stem and leaf plot, if the outlier is removed what is the new range?

Leaf
25
3
4
5
6
71\ 5\ 7\ 9
81\ 1\ 2\ 2\ 9
92\ 7

Key: 1|2 = 12

8

Consider the following stem and leaf plot:

a

Find the range of the data set.

b

Identify the outlier.

c

Find the new range of the data set with the outlier removed.

Leaf
51
65\ 8\ 8\ 8
73\ 3\ 8\ 8
83

Key: 1\vert 2 = 12

9

Consider the following stem and leaf plot:

a

Find the mean, correct to one decimal place.

b

Find the new range of the data set with the outlier removed.

Leaf
34\ 4\ 9
46\ 6\ 8\ 9
51\ 4
6
7
84

Key: 1\vert 2 = 12

10

The number of three-pointers scored in a basketball game are shown in the dot plot:

a

Find the range of the data.

b

If the outlier is removed what is the new range?

11

The number of tries in a series of rubgy tests are shown in the dot plot below.

The mode is 2, if the outlier is removed what is the new mode?

12

The glass windows for an airplane are rolled to a certain thickness, but machine production means there is some variation. The thickness of each pane of glass produced is measured (in millimetres), and the dot plot shows the results:

a

The current median is 11.15. If the outlier is removed what is the new median?

b

The current mean is 11.1. If the outlier is removed what is the new mean? Round your answer to two decimal places.

13

Consider the following frequency table:

If the outlier is removed what is the new mean? Round your answer to two decimal places if needed.

Weight in kilogramsFrequency
122
135
141
152
160
170
181
14

Consider the following frequency table:

If the outlier is removed what is the new mode?

Weight in kilogramsFrequency
141
150
160
173
186
194
202
15

For each of the following scenarios, determine whether the outlier that was removed must have had a value smaller or larger than the values that remain:

a

A set of data has an outlier removed and the mean lowers.

b

A set of data has an outlier removed and the mean rises.

c

A set of data has an outlier removed and the median lowers.

d

A set of data has an outlier removed and the median rises.

16

The selling price of recently sold houses are:

\$467\,000,\, \$413\,000,\, \$410\,000,\, \$456\,000,\, \$487\,000,\, \$929\,000

a

Find the mean selling price, to the nearest thousand dollars.

b

Which of the selling prices raises the mean so that it is not reflective of most of the prices?

c

Recalculate the mean selling price excluding this outlier.

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Outcomes

ACMSP207

Investigate the effect of individual data values, including outliers, on the mean and median

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