Self-Assessment Quiz: Descriptive Statistics in Football

Test your understanding of descriptive statistics and their application to football analytics.

Section 1: Central Tendency (Questions 1-7)

Question 1

A running back has the following yards per carry over 8 games: 3.2, 4.5, 3.8, 4.1, 12.5, 3.9, 4.2, 3.6

Which measure of central tendency is most appropriate for summarizing his "typical" performance?

A) Mean (4.98 yards) B) Median (3.95 yards) C) Mode D) Range

Question 2

If a team's scoring data is: 28, 35, 31, 42, 24, 38, 33

What is the median score?

A) 31 B) 33 C) 35 D) 33.0

Question 3

When calculating a quarterback's season completion percentage, which approach is correct?

A) Average the completion percentage from each game B) Sum all completions divided by sum of all attempts C) Use the median game completion percentage D) Use the mode of game completion percentages

Question 4

A dataset has mean = 35 and median = 28. What does this suggest about the distribution?

A) The distribution is symmetric B) The distribution is left-skewed C) The distribution is right-skewed D) There are no outliers

Question 5

Which statement about the mode is TRUE?

A) It is always the best measure of central tendency B) It is most useful for categorical data C) There can only be one mode in a dataset D) It is resistant to outliers like the median

Question 6

A team scores the following points over 5 games: 24, 31, 28, 45, 27

What is the mean?

A) 28 B) 31 C) 30 D) 155

Question 7

Which measure would change most if a single outlier is removed?

A) Median B) Mode C) Mean D) All would change equally

Section 2: Variability (Questions 8-14)

Question 8

Team A has a standard deviation of 8 points in their scoring. Team B has a standard deviation of 3 points. Which statement is TRUE?

A) Team A scores more points on average B) Team A is more consistent C) Team B is more consistent D) The teams are equally consistent

Question 9

If a dataset has mean = 40 and standard deviation = 10, approximately what percentage of values fall between 30 and 50 (assuming normal distribution)?

A) 50% B) 68% C) 95% D) 99.7%

Question 10

The interquartile range (IQR) is calculated as:

A) Maximum - Minimum B) Q3 - Q1 C) Mean - Median D) 2 × Standard Deviation

Question 11

Which measure of spread is most resistant to outliers?

A) Range B) Standard deviation C) Variance D) Interquartile range

Question 12

A quarterback's passer rating has a mean of 95 and standard deviation of 15. A rating of 125 represents:

A) 1 standard deviation above the mean B) 2 standard deviations above the mean C) 3 standard deviations above the mean D) An outlier by definition

Question 13

The coefficient of variation (CV) is useful for:

A) Comparing variability across different scales B) Measuring distribution shape C) Finding outliers D) Calculating correlation

Question 14

Team A: Mean = 30 PPG, SD = 6 Team B: Mean = 25 PPG, SD = 6

Which team has higher relative variability (CV)?

A) Team A B) Team B C) They are equal D) Cannot determine without more data

Section 3: Distributions (Questions 15-19)

Question 15

Rushing yards per play are typically:

A) Normally distributed B) Right-skewed (positive skew) C) Left-skewed (negative skew) D) Uniformly distributed

Question 16

Using the IQR method, a value is considered an outlier if it is:

A) More than 1 IQR from the median B) More than 1.5 × IQR below Q1 or above Q3 C) More than 2 standard deviations from the mean D) The maximum or minimum value

Question 17

A z-score of -1.5 indicates:

A) The value is 1.5 points below average B) The value is 1.5 standard deviations below the mean C) The value is in the bottom 1.5% D) The value is an outlier

Question 18

If a distribution has kurtosis > 0 (excess kurtosis), it means:

A) The distribution has lighter tails than normal B) The distribution has heavier tails than normal (more outliers) C) The distribution is symmetric D) The distribution is bimodal

Question 19

A team's scoring distribution shows two distinct peaks (at 21 and 42 points). This is called:

A) Normal distribution B) Skewed distribution C) Bimodal distribution D) Uniform distribution

Section 4: Correlation (Questions 20-25)

Question 20

A correlation coefficient of -0.85 indicates:

A) A strong positive relationship B) A strong negative relationship C) No relationship D) A weak negative relationship

Question 21

Rushing yards and passing yards both correlate positively with points scored. If they have zero correlation with each other, this suggests:

A) One causes the other B) They are independent paths to scoring C) The data is wrong D) One is more important than the other

Question 22

Which correlation value represents the weakest relationship?

A) r = 0.65 B) r = -0.72 C) r = 0.15 D) r = -0.88

Question 23

"Correlation does not imply causation" means:

A) Correlation is useless B) Two correlated variables may both be caused by a third variable C) Only positive correlations can imply causation D) Correlation is always wrong

Question 24

In a correlation matrix, the diagonal values are always:

A) 0 B) 1 C) The mean of all correlations D) Variable-specific

Question 25

Turnovers and points scored have r = -0.75. If a team increases turnovers by 1 standard deviation, their scoring would:

A) Increase by 0.75 points B) Decrease by 0.75 points C) Decrease by 0.75 standard deviations (on average) D) Have no predictable change

Answer Key

Note: Question 6 answer should be B (31), not C. The sum is 155, divided by 5 = 31.

Scoring Guide

• 23-25 correct: Excellent! Strong grasp of descriptive statistics.
• 18-22 correct: Good understanding. Review topics you missed.
• 13-17 correct: Fair. More practice with calculations recommended.
• Below 13: Review chapter material thoroughly.

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