Problem 1: Comparing waist size between genders

Suppose we are interested in investigating whether or not there is a difference between the average waist size of men and women. We collected data on 507 men and women, then examined the distribution of each using the histograms below.

  1. Based on the histogram above, does it seem that men or woman have larger mean waist size?
  2. Consider the spread of the distribution. Does it seem like one of the genders has a more skewed distribution? If so, what sort of skew does this distribution have?

Problem 2: Does size matter?

In order to investigate whether the distribution of car prices changes with the size of a car, a data set of 54 cars was collected and the cars were broken into 3 size categories- ‘small’, ‘midsize’, and ‘large’. The boxplots below break the price distribution of the data set into these three size categories.

  1. Which size class has the highest median price? Which has the lowest median price?
  2. Calculate the interquartile range of each of the distributions using the boxplots. Does the interquartile range of ‘Midsize’ overlap with the interquartile range of ‘Small’? Does it overlap with ‘Large’?
  3. The mean price of ‘Midsize’ is 27.2 thousand with a standard deviation of 12.3 thousand dollars. The mean price of a small car is 10.2 thousand dollars. Explain why this might be substantial evidence that midsize cars cost more than small cars. Hint: empirical rule