What can be inferred about a distribution that is skewed to the right?

What can be inferred about a distribution that is skewed to the right?

• A. The mean is less than the median
• B. The majority of data points are low
• C. The median is higher than the mean
• D. Most of the data points are clustered at the high end

Answer: (C)

A distribution skewed to the right, also known as positively skewed, typically has a longer tail on the right side. This characteristic results from a substantial number of lower values and only a few higher values that stretch the tail out towards the higher end of the number line. In such distributions, the mean is affected more by the extreme high values because it takes into account all data points, including the unusually high ones, while the median, which is the middle value when data is ordered, remains more resistant to these extremes. Therefore, in right-skewed distributions, the mean is usually greater than the median. With that in mind, the statement that the median is higher than the mean accurately reflects this pattern and captures the essence of the distribution's behavior. It indicates that while most values cluster towards the lower end, the presence of outliers on the higher end pulls the mean up, which is why the median (representative of the center of the data) is greater than the mean.

A distribution skewed to the right, also known as positively skewed, typically has a longer tail on the right side. This characteristic results from a substantial number of lower values and only a few higher values that stretch the tail out towards the higher end of the number line.

In such distributions, the mean is affected more by the extreme high values because it takes into account all data points, including the unusually high ones, while the median, which is the middle value when data is ordered, remains more resistant to these extremes. Therefore, in right-skewed distributions, the mean is usually greater than the median.

With that in mind, the statement that the median is higher than the mean accurately reflects this pattern and captures the essence of the distribution's behavior. It indicates that while most values cluster towards the lower end, the presence of outliers on the higher end pulls the mean up, which is why the median (representative of the center of the data) is greater than the mean.