Identify any outliers in each of the following data sets:
| Leaf | |
|---|---|
| 1 | 2 |
| 2 | 7\ 7\ 9\ 9 |
| 3 | 1\ 3\ 3\ 3\ 3\ 5\ 8 |
| 4 | 4\ 4\ 5 |
Key: 5 | 2 \ = \ 52 hours
The table shows the average temperature (\degree \text{C}) in a particular city over several years. State the year in which the temperature is an outlier.
| \text{Year} | 2 002 | 2 003 | 2 004 | 2 005 | 2 006 | 2 007 | 2 008 |
|---|---|---|---|---|---|---|---|
| \text{Temperature } (\degree \text{C}) | 32.7 | 26.5 | 22.6 | 22.5 | 24.2 | 23.0 | 24.1 |
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:
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:
What is the thinnest pane measured?
What thickness was measured 3 times?
Which thickness can be seen as an outlier?
The number of three-pointers scored in a basketball game are shown in the dot plot:
The mode is 2. If the outlier is removed, state the new mode.
Consider the given frequency table:
If the outlier is removed, state the mode.
| Weight in kilograms | Frequency |
|---|---|
| 14 | 1 |
| 15 | 0 |
| 16 | 0 |
| 17 | 3 |
| 18 | 6 |
| 19 | 4 |
| 20 | 2 |
Consider the following frequency table:
The current mean is 13.7.
Identify the outlier.
If the outlier is removed, will the new mean be higher or lower than the current mean?
If the outlier is removed, calculate the new mean, to one decimal place.
| Weight in kilograms | Frequency |
|---|---|
| 12 | 2 |
| 13 | 5 |
| 14 | 1 |
| 15 | 2 |
| 16 | 0 |
| 17 | 0 |
| 21 | 1 |
Consider the given stem-and-leaf plot:
The current mean is 48.50.
Identify the outlier.
If the outlier is removed, will the new mean be higher or lower than the current mean?
If the outlier is removed, calculate the new mean, to two decimal places.
| Leaf | |
|---|---|
| 3 | 4\ 4\ 9 |
| 4 | 6\ 6\ 8\ 9 |
| 5 | 1\ 4 |
| 6 | |
| 7 | |
| 8 | 4 |
Key: 2 \vert 3 = 23
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.
For each of the following sets of data:
Find the mean, median and mode. 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 three statistics changed after removing the outlier.
For each of the following scenarios, determine whether the outlier that was removed must have had a value smaller or larger than the scores 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.
When an outlier is removed from a data set, describe the effect on the following:
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.