Refer to Data Set #3 in the How Extreme Values Affect the Mean and Median applet. This applet loads with a dotplot for the following n = 5 observations: 27, 28, 32, 34, 37.

a. What are the mean and median for this data set?

b. Use your mouse to change the value x = 27 (the moveable green dot) to x = 25. What are the mean and median for the new data set?

c. Use your mouse to move the green dot to x = 5. When the smallest value is extremely small compared to the other observations, which is larger, the mean or the median?

d. At what value of x does the mean equal the median?

e. What are the smallest and largest possible values for the median?

f. What effect does an extremely small value have on the mean? What effect does it have on the median?