Question
Because of the existence of extremely wealthy individuals, economic data concerning income is very skewed. Which statement regarding the distribution of income is correct?
Question 2 options:
Due to the skew the median will be a better measure of center for this data than the mean
The standard deviation will be a good measure of spread for this data.
Each section of a boxplot will be about the same width.
Due to the skew the median is greater than the mean.
Question 2 options:
Due to the skew the median will be a better measure of center for this data than the mean
The standard deviation will be a good measure of spread for this data.
Each section of a boxplot will be about the same width.
Due to the skew the median is greater than the mean.
Answers
GPT-4o mini
The correct statement regarding the distribution of income in the context of extreme wealth is:
**Due to the skew, the median will be a better measure of center for this data than the mean.**
This is true because income distribution is typically right-skewed, meaning that a small number of individuals have extremely high incomes, which can disproportionately affect the mean. The median, being the middle value, is less affected by these outliers and provides a better measure of central tendency for skewed data.
The other statements are not correct:
- The standard deviation may not be a good measure of spread for skewed data due to its sensitivity to outliers.
- In a boxplot, the sections may not be of equal width in cases of skewness.
- In a right-skewed distribution, the mean is generally greater than the median, not the other way around.
**Due to the skew, the median will be a better measure of center for this data than the mean.**
This is true because income distribution is typically right-skewed, meaning that a small number of individuals have extremely high incomes, which can disproportionately affect the mean. The median, being the middle value, is less affected by these outliers and provides a better measure of central tendency for skewed data.
The other statements are not correct:
- The standard deviation may not be a good measure of spread for skewed data due to its sensitivity to outliers.
- In a boxplot, the sections may not be of equal width in cases of skewness.
- In a right-skewed distribution, the mean is generally greater than the median, not the other way around.