Which property is shared by both the mean and the median?

Which property is shared by both the mean and the median?

• A. Uniqueness
• B. Not affected by extreme values
• C. Simplicity
• D. A measure of dispersion

Answer: (A)

Both the mean and the median give a single central value for a data set. The mean is computed by summing all observations and dividing by how many there are, which always yields one number. The median is found by ordering the data and taking the middle value; if there are an even number of observations, you take the average of the two middle ones. In every case you end up with a single, well-defined summary of the center for that data set. For example, with data 1, 2, 3, 1000, the mean is 251.5 and the median is 2.5, each a single number. This is why “uniqueness” is the common property these two share. The other options don’t fit: the mean changes with extreme values while the median stays relatively stable, so they don’t share a property about being unaffected by outliers; neither statistic is a measure of dispersion, since they summarize center, not spread; and simplicity isn’t guaranteed to be shared by both.

Both the mean and the median give a single central value for a data set. The mean is computed by summing all observations and dividing by how many there are, which always yields one number. The median is found by ordering the data and taking the middle value; if there are an even number of observations, you take the average of the two middle ones. In every case you end up with a single, well-defined summary of the center for that data set. For example, with data 1, 2, 3, 1000, the mean is 251.5 and the median is 2.5, each a single number. This is why “uniqueness” is the common property these two share. The other options don’t fit: the mean changes with extreme values while the median stays relatively stable, so they don’t share a property about being unaffected by outliers; neither statistic is a measure of dispersion, since they summarize center, not spread; and simplicity isn’t guaranteed to be shared by both.