Statistics Unit

2.8 Measures of Variation




  1. Suppose that Samira records the ages of customers at the Snack Bar on a college campus from 12-2pm tomorrow, while Mary records the ages of customers at the McDonald’s near the highway at the same time. Who will have the larger SD of their ages – Samira or Mary? Explain why.

    Mary is likely to encounter people of all ages at McDonald’s – from toddlers to senior citizens and every age in between. Samira might run into some toddlers and senior citizens at the on-campus snack bar, but she’ll mostly find a lot of people in the 18-25-year-old age group. Because the ages of McDonald’s customers will vary more than ages of Snack Bar customers, Mary will have a larger standard deviation of ages than Samira will.

  2. Suppose that Carlos and Hector visit their local humane society animal shelter. Carlos records the weights of the 25 cats that they find there, and Hector records the weights of the 25 human beings that they encounter. Who will have the larger standard deviation of their weights –Carlos or Hector?

    The weights of human beings vary much more than the weights of ordinary domestic cats, so Hector will have a larger standard deviation than Carlos.

The World's Highest-Paid Athletes 2025

Rank Name Total Earnings Salary/Winnings Endorsements Sport
#1 Christiano Ronaldo $260 M $200 M $60 M Soccer
#2 Canelo Alvarez $137 M $125 M $12 M Boxing
#3 Lionel Messi $130 M $60 M $70 M Soccer
#4 Juan Soto $129.2 M $122.2 M $7 M Baseball
#5 LeBron James $128.7 M $48.7 M $80 M Basketball
#6 Karim Benzema $115 M $110 M $5 M Soccer
#7 Stephen Curry $105.4 M $55.4 M $50 M Basketball
#8 Shohei Ohtani $102.5 M $2.5 M $100 M Baseball
#9 Kevin Durant $100.8 M $50.8 M $50 M Basketball
#10 John Rahm $100.7 M $84.7 M $16 M Golf
#11 Lewis Hamilton $100 M $70 M $30 M Car Racing
#12 Kylian Mbappe $95 M $70 M $25 M Soccer
#13 Giannis Antetokounmpo $94.3 M $49.3 M $45 M Basketball
#14 Rory McIlroy $91.2 M $36.2 M $55 M Golf
#15 Max Verstappen $83 M $75 M $8 M Car Racing
#16 Scottie Scheffler $82.9 M $50.9 M $32 M Baseball

Source Sportico

TOTAL EARNINGS

Mean:

$115.98 M

Median:

$101.65 M

Mode:

No mode

Range:

$177.1 M

Quartiles

Low (Min):

$82.9 M

Lower Quartile (Q1):

$94.65 M

Median (Q2):

$101.65 M

Upper Quartile (Q3):

$128.95

High (Max):

$260 M

BOXPLOT

The title of the box plot is The World's Highest Paid Athletes 2025. The x-axis on the box plot is numbered from 80 to 260, counting by 20, and labeled Total Earnings in Millions of Dollars. The left whisker is at 82.9, the minimum number, and the right whisker is at 260, the maximum number. The box that is drawn contains the lower quartile at 94.65, the median at 101.65 and the upper quartile at 128.95.

Standard Deviation:

$41.98 M

ENDORSEMENTS

Mean:

$40.31 M

Median:

$38.5 M

Mode:

$50 M

Range:

$95 M

Quartiles

Low (Min):

$5 M

Lower Quartile (Q1):

$14 M

Median (Q2):

$38.5 M

Upper Quartile (Q3):

$57.5 M

High (Max):

$100 M

BOXPLOT

The box plot is titled The World's Highest Paid Athletes 2025. The x-axis is Endorsements in millions of dollars and goes from 0 to 100, counting by 10. The left whisker is at 5, the minimum number, and the right whisker is at 100, the maximum number. The box that is drawn contains the lower quartile at 14, the median at 38.5 and the upper quartile at 57.5.

Standard Deviation:

$28.33 M