Distributions of univariate data questions require knowledge of the following topics: mean, median, range, interquartile range, standard deviation, quartiles, percentile range and boxplots.

Examples of AP Statistics multiple choice questions with distributions of univariate data:

1. Two distributions D_{1} and D_{2} are displayed on the same graph. If the distribution D_{1} is right skewed, the distribution D_{2} is left skewed, and the mean of D_{1} is lower than the mean of D_{2}, which of the following statements is not true?

a) The median of D_{1} is lower than the median of D_{2}. b) The mean of D_{1} is lower than the median of D_{2}. c) The mean of D_{2} is lower than the median of D_{1}. d) The median of D_{1} is lower than the mean of D_{2}. e) The mean of D_{2} is lower than the median of D_{2}.

Since the distribution D_{1} is right skewed, the distribution D_{2} is left skewed, and the mean of D_{1} is lower than the mean of D_{2}, we can draw the two
distributions on the same plot, as seen above. We notice that the only statement that is not correct is c).

2. The mean of the weights of a group of 100 men and women is 160lb. If the number of men in the group is 60 and the mean weight of the men is 180lb, what is the mean weight of the women?

a) 120lb b) 125lb c) 130lb d) 132lb e) 135lb

We know that 60 men have a mean weight of 180lb, so the sum of the men's weights is Σ(wm) = 60 · 180lb = 10,800lb.
The total weight of all men and women is Σ(wm + ww) = 100 · 160lb = 16,000lb. By subtracting 10,800lb from 16,000lb, we obtain the total weight of all women: Σ(ww) = 5,200lb.
The mean weight of the women is equal to Σ(ww)/40 = 5,200lb/40 = 130lb, and c) is the correct answer.

3. It takes different times for different workers to perform the same specific task, as it is shown in the distribution below.
Which of the following statements must be true?

a) the 25th percentile is greater than 70 minutes. b) the distribution is skewed to the left. c) the interquartile range is higher than 20 minutes. d) distribution median < distribution mean. e) distribution median = distribution mean.

We notice that the distribution is skewed to the left. A left skewed dstribution has the distribution median > distribution mean,
so answers d) and e) are incorrect. The 25^{th} percentile is lower than 70 minutes and the interquartile range is
lower than 20 minutes.