1.5 Measures of Relative Standing
The World's Highest-Paid Athletes 2022
Open the data set in Stat Crunch “The World’s Highest Paid Athletes 2022”:
Source Highest Paid Athletes List From Forbes
- Identify the following statistical measures for Total Pay:
- Mean:
$90.23 M - Standard Deviation:
$18.89 M M - Mode:
68 - Minimum:
$68 M - Lower Quartile (Q1):
$74.4 M - Median:
$90 M - Upper Quartile (Q3):
$95 M - Max:
$130 M - Range:
$62 M
- Mean:
- Label the Quartiles on the box plot for Total Pay:
- Determine the Inter-Quartile Range (IQR) for Total Pay:
$20.6 M The range of the “middle” 50% of the data is called the interquartile range.
- How many of the world’s fifteen highest paid athletes for 2022 earned a total pay greater than $95 million?
3 - How many of the world’s fifteen highest paid athletes for 2022 earned a total pay less than $74.4 million?
3 - How many of the world’s fifteen highest paid athletes for 2022 earned a total pay between $90 million and $95 million?
3 - Use Stat Crunch to compare box plots for On-the-Field Earnings and Off-the-Field Earnings.
- Which data set has a higher median?
Off-the-field - Which data set has a greater range?
Off-the-field - In which data set do 50% of the athletes earn between $25 million and $55 million?
Off-the-field - Which data set has more athletes earning more than $60 million?
On-the-field - Overall, would you say the world’s highest paid athletes earn more on-the-field or off-the-field? Use characteristics of the boxplots to explain your choice.
You might say that overall athletes earn more on-the-field since the middle 50% earn between about $40 million and $70 million.
- Which data set has a higher median?
- Lower Outlier Critical Value:
\(Q_1 - 1.5(IQR)\) - Upper Outlier Critical Value:
\(Q_3 + 1.5(IQR)\) - Are there any outliers in the Total Pay data set?
Yes, Lionel Messi’s total pay of $130 million is an outlier. - What is the lower outlier critical value for the Total Pay data set?
74.4 – 1.5(20.6) = 43.5 million - Are there any data values in the Total Pay data set that are less than your answer to part (a)?
no - What is the upper outlier critical value for the Total Pay data set?
95 + 1.5(20.6) = 125.9 million - Are there any data values in the Total Pay data set that are greater than your answer to part (c)?
yes
- What is the lower outlier critical value for the Total Pay data set?
- Are there any outliers in the On-the-Field data set?
no - The accompanying box-and-whisker plot represents the cost, in dollars, of twelve CD’s.
- Which cost is the upper quartile?
- What is the range of the costs of the CD’s?
- What is the median?
- Which cost represents the 100th percentile?
- How many CD’s cost between $14.50 and $26.00?
- How many CD’s cost less than $14.50?
$26
$22
$20.50
$29
6
3
- What percentage of values in the data set shown are greater than 6?
- 25%
- 50%
- 75%
- 100%
a. 25%
-
A movie theater recorded the number of tickets sold daily for a popular movie during the month of June. The box-and-whisker plot shown below represents the data for the number of tickets sold, in
hundreds.
- Which conclusion can be made using this plot?
- The second quartile is 600.
- The mean of the attendance is 400.
- The range of the attendance is 300 to 600.
- Twenty-five percent of the attendance is between 300 and 400.
iv. Twenty-five percent of the attendance is between 300 and 400.
- Of the following ranges of daily tickets sales, which range of ticket sales occurred more often than the others?
- 100-300
- 300-500
- 400-600
- 600-900
ii. 300-500 more than 25% of the daily ticket sales.
- Which conclusion can be made using this plot?
- The accompanying box-and-whisker plots can be used to compare the annual incomes of three professions.
- Based on the box-and-whisker plots, which statement is true?
- The median income for nuclear engineers is greater than the income of all musicians.
- The median income for police officers and musicians is the same.
- All nuclear engineers earn more than all police officers.
- A musician will eventually earn more than a police officer.
ii. The median income for police officers and musicians is the same.
- At least how much income do 75% of musicians earn per year?
$20,000
- Based on the box-and-whisker plots, which statement is true?
Outliers:
In our course, outliers are defined as data values outside the boundaries of the max and min outlier critical values. Give the formulas for the outlier critical values: