Consider two data sets A and B The sets are identical except

Consider two data sets A and B. The sets are identical except the high value of the data set B is three times greater than the high value of data set A.

(a) How do the median of the two data sets compare?
(b) How do the means of the two data sets compare?
(c) How do the standard deviations of the two data sets compare?
(d) How do the box- and

Solution

a. The medians are the same, because the median is the value such that 50% of the data points are higher and 50% are lower. The actual value of the highest element does not affect the median.

b. The mean of set B is greater.

c. The standard deviation of B is greater because the highest element is further from the mean.

d. The boxes are the same if the center line is the median because the interquartile range is the same. However, the upper whisker on B is longer to reflect that the highest value is greater. (It may be one of the outliers.)