Question

Describe a Variable Describe one quantitative variable that you believe will give data that are skewed to the right, and explain your reasoning. Do not use a variable that has already been discussed.

Short answer

A quantitative variable that might be skewed to the right is 'age at death in developed countries'. The reason is that while most people die at an age in the 70s or 80s, a significant minority live significantly longer, even up to 100 and above. This creates a distribution where the mean is pulled in the direction of these high values, causing a rightwards skew.

Step-by-step solution

Understanding 'Skewness'

Skewness is a measure of the asymmetry of the data around the sample mean. If the data set is not perfectly symmetrical, then it is either 'skewed left' (negative skewness) or 'skewed right' (positive skewness). Left-skewed data is dominated by lower scale values, while right-skewed data is dominated by higher scale values with a few extremely high values.

- Select a Quantitative Variable Skewed to the Right

A classic example of a variable that may be 'skewed right' is age at death in developed countries. Most people live to their seventies or eighties, creating a mode in that range. However, a significant number live past that age, creating a long tail to the right of the distribution.

- Justify the Selection

The reasoning behind the selected variable being skewed to the right is that, while the life expectancy in developed countries is in the 70s or 80s, there are people who live far beyond that age, even up to 100 and above. These high age values pull the mean of the data to the right so that it is greater than the median, hence the right skewness.