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 line plot shows the results:
What is the thinnest pane measured?
What thickness was measured 3 times?
If the glass is more than 0.1 \text{ mm} outside the ideal thickness of 11.1 \text{ mm}, it is not used. How many of the panes measured can be used?
What proportion of windows can be used?
Which thickness can be seen as an outlier?
The number of three-pointers scored in a basketball game are shown in the line 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.
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.
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 line 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.
Which measure of centre would be best for the following data set?
State the most appropriate measure of centre for the following scenarios:
For a particular street in Sydney, house prices for houses sold in the last 36 months (in 1000's) were given:
920,\, 920,\, 709,\, 694,\, 667,\, 657,\, 630,\, 610,\, 584,\, 567,\, 555
The number of animal races that were won by a trainer over the years shown are listed in the table:
| Year | 2003 | 2004 | 2005 | 2006 | 2007 |
|---|---|---|---|---|---|
| Races won | 116 | 105 | 102 | 108 | 113 |
The number of minutes spent studying by each member of a group of students is given:
85,\, 85,\, 95,\, 70,\, 60,\, 70,\, 105
A netball team has so far played 8 games in the season. Their final score in each game is given:
36,\, 46,\, 49,\, 40,\, 52,\, 44,\, 39,\, 37
The number of songs Oprah has downloaded in each of the last seven months is given:
6,\, 12,\, 18,\, 9,\, 0,\, 3,\, 15
The selling price of recently sold houses is given below:
\$760\,000,\, \$650\,000,\, \$810\,000,\, \$780\,000,\, \$760\,000,\, \$590\,000,\, \$1\,360\,000
Find the mean selling price. Round your answer to the nearest thousand dollars.
Find the median selling price.
Recalculate the mean selling price excluding the outlier.
Recalculate the median selling price excluding the outlier.
Which measure of centre best identifies the typical selling price of recently sold houses? Explain your answer.
The weight of fish caught in a "weigh and release" fishing competition, in kilograms are given below:
12.5,\, 15.1,\, 13,\, 14.2,\, 14.5,\, 14.9,\, 12.5,\, 14.3,\, 1.5
Find the mean weight.
Find the median weight.
Recalculate the mean weight excluding the outlier.
Recalculate the median weight excluding the outlier.
Which measure of centre best identifies the typical fish weight? Explain your answer.
Consider the histogram shown. Which measure(s) of centre best represents the centre of the data set? Explain your answer.
Carl has been recording his spelling test scores for the past semester. His scores were:14,\, 16,\, 2,\, 15,\, 15,\, 16,\, 15
Calculate the median of Carl's scores.
Calculate the mean of Carl's scores, to two decimal places.
Which measure of centre most accurately describes the centre of this data set? Explain your answer.
The salaries of part-time employees at a company are given in the dot plot below. Which measure of centre best reflects the typical wage of a part-time employee? Explain your answer.
The age of students that participated in extra-curricular activities were recorded, and their results are presented in the line plot below:
Find the mean age of participation among the sample of students.
Find the median age of participation among the sample of students.
By looking at the line plot, are the mean and median representative measures for the age of the typical student who participates in activities? Explain your answer.
A journalist wanted to report on road speed cameras being used as revenue raisers. She obtained data that showed the number of times 20 speed cameras issued a fine to motorists in one month. The results were:
101,\, 102,\, 115,\, 115,\, 121,\, 124,\, 127,\, 128,\, 130,\, 130,\\ 143,\, 143,\, 146,\, 162,\, 162,\, 163,\, 178,\, 183,\, 194,\, 977
The journalist wants to give the impression that speed cameras are just being used to raise revenue. Which measure of centre should she use in her article? Explain your answer.