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 2023

Rank Name Total Earnings Salary/Winnings Endorsements Sport
#1 Christiano Ronaldo $275 M $215 M $60 M Soccer
#2 Jon Rahm $203 M $181 M $22 M Golf
#3 Lionel Messi $130 M $65 M $65 M Soccer
#4 Lebron James $125.7 M $45.7 M $80 M Basketball
#5 Kyliam Mbappe $125M $100 M $25 M Soccer
#6 Neymar $121 M $86 M $35 M Soccer
#7 Stephen Curry $98.9 M $48.9 M $50 M Basketball
#8 Giannis Antetokounmpo $88.4 M $43.4 M $45 M Basketball
#9 Kevin Durant $86.9 M $44.9 M $42 M Basketball
#10 Patrick Mahomes $84.3 M $59.3 M $25 M Football
#11 Lamar Jackson $82.5 M $80 M $2.5 M Football
#12 Karim Benzema $78 M $70 M $8 M Soccer
#13 Rory McIlroy $77.4 M $37.4 M $40 M Golf
#14 Tiger Woods $77.2 M $12.2 M $65 M Golf
#15 Max Verstappen $75 M $70 M $5 M Car Racing
#16 Shohei Ohtani $70 M $30 M $40 M Baseball

Source Sportico

TOTAL EARNINGS

Mean:

$112.39 M

Median:

$87.65 M

Mode:

No mode

Range:

$205 M

Quartiles

Low (Min):

$70 M

Lower Quartile:

$77.7 M

Median:

$87.65 M

Upper Quartile:

$125.35

High (Max):

$275 M

BOXPLOT

The title of the box plot is Total Earnings. The x-axis on the box plot is numbered from 60 to 280, counting by 20, and labeled Millions of Dollars. The left whisker is at 70, the minimum number, and the right whisker is at 275, the maximum number. The box that is drawn contains the lower quartile at 77.7, the median at 87.65 and the upper quartile at 125.35.

Standard Deviation:

$54.96 M

Mean:

$38.1 M

Median:

$40 M

Mode:

$25, 40, 65 M

Range:

$77.5 M

Quartiles

Low (Min):

$2.5 M

Lower Quartile:

$23.5 M

Median:

$40 M

Upper Quartile:

$55 M

High (Max):

$80 M

BOXPLOT

The box plot is titled Off-the-field Earnings. The x-axis is in millions of dollars and goes from 0 to 95, counting by 5. The left whisker is at 2.5, the minimum number, and the right whisker is at 90, the maximum number. The box that is drawn contains the lower quartile at 25, the median at 47 and the upper quartile at 55.

Standard Deviation and Range Rule of Thumb for Standard Deviation:

$22.8 M and $19.4 M