Which statement best describes the median and when it is preferred over the mean?

Which statement best describes the median and when it is preferred over the mean?

• A. The middle value of ordered data.
• B. The middle value (or average of the two middle values); preferred when data are skewed or contain outliers.
• C. The most frequent value.
• D. The difference between the maximum and minimum values.

Answer: (B)

The median is the middle value in an ordered set of data (and for an even number of observations, the average of the two middle values). It is preferred when data are skewed or contain outliers because it isn’t pulled toward extreme values. This makes it a better representative of a "typical" observation in such cases. For example, in income data, a few very high salaries can raise the average, but the median remains near the center of most people’s earnings. When the data are roughly symmetric, the mean and median are similar, but the median provides a more robust measure of central tendency in the presence of skewness or outliers.

The median is the middle value in an ordered set of data (and for an even number of observations, the average of the two middle values). It is preferred when data are skewed or contain outliers because it isn’t pulled toward extreme values. This makes it a better representative of a "typical" observation in such cases. For example, in income data, a few very high salaries can raise the average, but the median remains near the center of most people’s earnings. When the data are roughly symmetric, the mean and median are similar, but the median provides a more robust measure of central tendency in the presence of skewness or outliers.