Sampling & Data
What is the difference between qualitative and quantitative data?
Qualitative data describes categories or characteristics, while quantitative data represents numerical values.
What is the probability of rolling a 6 on a fair six-sided die?
1/6
What is the formula for finding the mean of a dataset?
Sum of all values divided by the number of values.
What type of graph is best for showing the distribution of a single quantitative variable?
Histogram
In baseball statistics, what does OBP stand for?
On-base percentage
Give an example of a biased sample.
Surveying only students in an AP math class about their feelings on school-wide math requirements.
A bag contains 3 red, 5 blue, and 2 green marbles. What is the probability of drawing a blue marble?
5/10 or 1/2
What is the median of this dataset: 5, 7, 9, 12, 15, 18, 21?
12
What does a box plot show that a histogram does not?
The five-number summary (minimum, Q1, median, Q3, maximum)
What is a key statistic that the Oakland A’s used in "Moneyball" to evaluate players?
On-base percentage (OBP)
What is the difference between an observational study and an experiment?
In an observational study, researchers do not manipulate variables; in an experiment, they apply treatments and study the effects.
If you flip a coin 3 times, what is the probability of getting exactly 2 heads?
3/8
Find the mode of this dataset: 2, 4, 4, 7, 8, 8, 8, 10, 12.
8
What does the height of a bar in a bar chart represent?
The frequency or count of a category
What sport relies heavily on expected goals (xG) to predict performance?
Soccer
What is the term for when a sample is chosen in such a way that every individual has an equal chance of being selected?
Random sampling
What is the probability of drawing two aces in a row from a standard deck of 52 cards?
(4/52) * (3/51) = 1/221
What measure of spread is found by subtracting the smallest value from the largest?
Range
What type of graph is best for comparing proportions in categorical data?
Pie chart
In football (NFL), what does QBR measure?
Quarterback rating, a composite statistic to measure overall performance
What is stratified sampling, and why is it useful?
Stratified sampling divides the population into groups (strata) and randomly selects from each group to ensure representation.
You roll two dice. What is the probability that the sum is 7?
6/36 or 1/6
What is the standard deviation a measure of?
The amount of variation or spread in a dataset.
What can a scatter plot show us about two variables?
A correlation or trend between them (positive, negative, or no correlation)
In sports analytics, what is the main advantage of using advanced statistics over traditional stats like points or wins?
Advanced statistics provide deeper insights into player performance by accounting for factors like efficiency, context, and contribution to team success rather than just raw totals.