10.05 Outliers
Identify the outlier in the following data sets:
5, \,6, \,7, \,8, \,9, \,9, \,18
59, \,61, \,63, \,70, \,73, \,76, \,113
10, \,7, \,6, \,8, \,1, \,10, \,6
73, \,65, \,72, \,68, \,74, \,57, \,121
Identify the outlier(s) in the following data sets:
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, \,63Rochelle 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
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
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:
For each of the following sets of data identify the outlier(s):
| Hours per week | |
|---|---|
| 1 | 1 |
| 2 | 6\ 7\ 9 |
| 3 | 1\ 2\ 2\ 4\ 4\ 5\ 6\ 7\ 8\ 9 |
| 4 | 1 |
Key: 5\vert 2 = 52 hours
| Leaf | |
|---|---|
| 2 | 3 |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | 1\ 3\ 5\ 8 |
| 8 | 1\ 3\ 3\ 4\ 5 |
| 9 | 3\ 4 |
Key: 1|2=12
For each of the following sets of data:
Find the mean, median, mode, and range. Round your answers to two decimal places where necessary.
Identify the outlier.
Remove the outlier from the set and recalculate the values found in part (i).
Describe how each of the four statistics changed after removing the outlier.
When an outlier is removed from a data set, describe the effect on the following:
Consider this stem and leaf plot, if the outlier is removed what is the new range?
| Leaf | |
|---|---|
| 2 | 5 |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | 1\ 5\ 7\ 9 |
| 8 | 1\ 1\ 2\ 2\ 9 |
| 9 | 2\ 7 |
Key: 1|2 = 12
Consider the following stem and leaf plot:
Find the range of the data set.
Identify the outlier.
Find the new range of the data set with the outlier removed.
| Leaf | |
|---|---|
| 5 | 1 |
| 6 | 5\ 8\ 8\ 8 |
| 7 | 3\ 3\ 8\ 8 |
| 8 | 3 |
Key: 1\vert 2 = 12
Consider the following stem and leaf plot:
Find the mean, correct to one decimal place.
Find the new range of the data set with the outlier removed.
| Leaf | |
|---|---|
| 3 | 4\ 4\ 9 |
| 4 | 6\ 6\ 8\ 9 |
| 5 | 1\ 4 |
| 6 | |
| 7 | |
| 8 | 4 |
Key: 1\vert 2 = 12
The number of three-pointers scored in a basketball game are shown in the dot plot:
Find the range of the data.
If the outlier is removed what is the new range?
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?
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:
The current median is 11.15. If the outlier is removed what is the new median?
The current mean is 11.1. If the outlier is removed what is the new mean? Round your answer to two decimal places.
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 kilograms | Frequency |
|---|---|
| 12 | 2 |
| 13 | 5 |
| 14 | 1 |
| 15 | 2 |
| 16 | 0 |
| 17 | 0 |
| 18 | 1 |
Consider the following frequency table:
If the outlier is removed what is the new mode?
| Weight in kilograms | Frequency |
|---|---|
| 14 | 1 |
| 15 | 0 |
| 16 | 0 |
| 17 | 3 |
| 18 | 6 |
| 19 | 4 |
| 20 | 2 |
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 set of data has an outlier removed and the mean lowers.
A set of data has an outlier removed and the mean rises.
A set of data has an outlier removed and the median lowers.
A set of data has an outlier removed and the median rises.
The selling price of recently sold houses are:
\$467\,000,\, \$413\,000,\, \$410\,000,\, \$456\,000,\, \$487\,000,\, \$929\,000
Find the mean selling price, to the nearest thousand dollars.
Which of the selling prices raises the mean so that it is not reflective of most of the prices?
Recalculate the mean selling price excluding this outlier.