Find the outlier(s) in the following data sets:
The stem and leaf plot shows the number of hours worked per week by a group of people. State the outlier.
| Number of hours | |
|---|---|
| 1 | 2 |
| 2 | 7\ 7\ 9\ 9 |
| 3 | 1\ 3\ 3\ 3\ 3\ 5\ 8 |
| 4 | 4\ 4\ 5 |
The dot plot shows the temperature \degree C in a town over a several week period. State the temperature that is an outlier.
The table shows the average temperature \degree C in a particular city over several years. State the year in which the temperature is an outlier.
| Year | 2 002 | 2 003 | 2 004 | 2 005 | 2 006 | 2 007 | 2 008 |
|---|---|---|---|---|---|---|---|
| Temperature (°C) | 31.7 | 26.5 | 22.6 | 22.5 | 24.2 | 23.0 | 24.1 |
State the coordinates of the outlier on the following graph:
For each of the following data sets, calculate:
The interquartile range
The value of the lower fence
The value of the upper fence
| \text{Minimum} | 5 |
|---|---|
| \text{Q}1 | 6 |
| \text{Median} | 12 |
| \text{Q}3 | 17 |
| \text{Maximum} | 28 |
Consider the given dot plot:
Find the:
Median
Lower quartile
Upper quartile
Interquartile range
Value of the lower fence
Value of the upper fence
Identify any outliers.
For each of the following sets of data:
Construct the five-number summary.
Calculate the interquartile range.
Calculate the value of the lower fence.
Calculate the value of the upper fence.
Would the value -5 be considered an outlier?
Would the value 16 be considered an outlier?
9,\, 5,\, 3,\, 2,\, 6,\, 1
3,\, 10,\, 9,\, 2,\, 7,\, 5,\, 6
12,\, 5,\, 11,\, 1,\, 9,\, 8,\, 5,\, 6
For each of the following sets of data:
Construct the five-number summary.
Would the value -3 be considered an outlier?
Would the value 15 be considered an outlier?
1,\, 4,\, 8,\, 10,\, 6,\, 2,\, 5
9,\, 4,\, 6,\, 11,\, 10,\, 8,\, 10
For each of the data sets below:
Construct the five-number summary.
Calculate the value of the lower fence.
Calculate the value of the upper fence.
Identify any outliers.
Create a box plot of the data with the outlier(s) displayed separately.
There is a test to measure the Emotional Quotient (EQ) of an individual. Here are the EQ results for 21 people listed in ascending order:
58, 90, 91, 92, 93, 94, 95, 95, 95, 97, 99, 100, 108, 114, 116, 116, 117, 118, 118, 122, 129
Find the median EQ score.
Find the Upper Quartile score.
Find the Lower Quartile score.
Find the interquartile range.
Find the lower fence.
Find the upper fence.
Use the fences to state any outliers.
Consider the data sets below:
Set A: \, 14,\, 18,\, 21,\, 19,\, 12,\, 16,\, 22,\, 20,\, 19,\, 13,\, 21,\, 20,\, 16,\, 7,\, 18,\, 20,\, 11,\, 19,\, 17,\, 24
Set B: \, 17,\, 9,\, 15,\, 24,\, 14,\, 13,\, 16,\, 10,\, 21,\, 14,\, 15,\, 17,\, 16,\, 13,\, 9,\, 19,\, 14,\, 18,\, 15,\, 12
Construct the five-number summary for each set.
Identify any outliers and use statistical calculations to justify your answer.
Create a parallel box plot of the data sets with the outlier(s) displayed separately.
The data point 5 is below the lower fence and is considered an outlier. The interquartile range is 12.
Find the smallest integer value the lower quartile can be.
The data point 37 is above the upper fence and is considered an outlier. The interquartile range is 10.
Find the largest integer value the upper quartile can be.
A group in a study take a test to assess their reaction time. The participants clicked a button as soon as they heard a sound which was played at random intervals. The reaction time, in milliseconds, of each participant is shown below:
220,\, 280,\, 210,\, 220,\, 215,\, 180,\, 185,\, 190,\, 190,\, 195,\, 150 \, 190,\, 195,\, 195Construct the five-number summary.
Identify any outliers and use statistical calculations to justify your answer.
Create a box plot of the data with the outlier displayed separately.
Give a possible explanation for the outliers present.
\text{VO}_{2} Max is a measure of how efficiently your body uses oxygen during exercise. The more physically fit you are, the higher your \text{VO}_{2} Max.
Here are some people’s results when their \text{VO}_{2} Max was measured:
46,\, 27,\, 32,\, 46,\, 30,\, 25,\, 41,\, 24,\, 26,\, 29,\, 21,\, 21,\, 26,\, 47,\, 21,\, 30,\, 41,\, 26,\, 28,\, 26,\, 76
Sort the values into ascending order.
Determine the median \text{VO}_{2} Max.
Determine the upper quartile value.
Determine the lower quartile value.
Calculate 1.5 \times IQR, where IQR is the interquartile range.
Identify any outliers using upper and lower fences.
Create a box plot of the data with the outlier displayed separately.
An average untrained healthy person has a \text{VO}_{2} Max between 30 and 40.
Using the boxplot, what level of exercise is likely to describe the majority of people in this group?
The number of three-pointers scored in a basketball game are shown in the given dot plot. The current mode is 2. If the outlier is removed, find the new mode.
For the given dot plot, the current range is 11. If the outlier is removed, find the new range.
Consider the given stem plot:
If the outlier is removed what is the new mean? Round your answer 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
Consider the given stem plot:
If the outlier is removed find the new range.
| Leaf | |
|---|---|
| 2 | 5 |
| 3 | |
| 4 | 9\ 9 |
| 5 | 0\ 0\ 4\ 5\ 7 |
| 6 | 2\ 6 |
Key: 1 | 2 \ = \ 12
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 |
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, 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.
True or False: When the outlier is removed from a set of data, the range will always decrease.
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.
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.
Seven millionaires with an average net wealth of \$41 million with a standard deviation of \$7 million are having a party. Suddenly Carlos Slim, who has a net wealth estimated to be \$31 billion, walks into the room.
What is the new average net wealth (in millions) in the room? Give your answer rounded to the nearest million.
When Carlos Slim's net worth is taken into account, will the standard deviation be higher, lower or unchanged from before?
Will the mode be higher, lower or unchanged from before if at least two of the millionaires have the same net wealth?
Will the range be higher, lower or unchanged from before?
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.
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 dot 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 dot plot, are the mean and median reliable 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.
The selling prices of artworks sold at an auction are given below:
\$18\,000,\, \$11\,000,\, \$17\,000,\, \$20\,000,\, \$18\,000,\, \$16\,000,\, \$15\,000,\, \$218\,000
Which measure of centre best identifies the typical selling price of recently sold artwork? Explain your answer.