## Distributions of Univariate Data

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}.

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

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.