1.55) For each of the following, state whether you expect the distribution to be symmetric, right skewed, or left skewed. Also specify whether the mean or median would best represent a typical observation in the data, and whether the variability of observations would be best represented using the standard deviation or IQR. Explain your reasoning.

  1. Number of pets per household.

Right Skewed

Many people have zero or very few pets. You cannot have fewer than zero pets so there is a fixed minimum. However some outliers have many pets. Since it is not symmetric and there are some people with 30 cats (skews right), the median would best represent a typical observation and the IQR would best represent the variability of observations.

  1. Distance to work, i.e. number of miles between work and home.

Right skewed

There is a minimum distance of 0 for those who work from home and some people work very far from home. Since it skews right, the median would best represent a typical observation and the IQR would best represent the variability of observations.

  1. Heights of adult males.

symmetric

There are a large number of men around the mean height and fewer as you go both above and below the mean height. Since it is symmetric, the mean would best represent a typical observation and the standard deviation would best represent the variability of observations.