Question

Online Cat Videos In Exercise 1.59 on page 28 , we introduced a study looking at the effect of watching cat videos on mood and energy. The authors asked participants how many cats they currently own and report 2.39 as the measure of center for this right-skewed distribution. (a) Is this measure of center the mean number of cats or the median number of cats? (Hint: Think about how the two numbers are calculated.) (b) Would we expect the mean number of cats to be greater than or less than the median?

Short answer

The measure 2.39 represents the mean number of cats. As it is a right-skewed distribution, the mean number of cats would likely be higher than the median.

Step-by-step solution

Understand key concepts

Understand the key concepts of mean and median. The mean is calculated by summing all numbers in a data set and dividing by the number of values, while the median is simply the middle value of the ordered data set.

Analyze the data distribution

Recognize that the data distribution is right-skewed, which means that extreme values on the right tail have a significant influence on the mean, making it larger than the median.

Identify the measure of center

Given the mentioned tendencies in right skewed distributions, it can be concluded that the reported 2.39 as a measure of center must be the mean.

Predict mean and median relation

Following the properties of a right-skewed distribution, it can be expected that the mean number of cats is greater than the median.