Grouped data Suppose that the data on heights provided in Exercise 34 had been organized into only six bins, as follows:

a) If you no longer had the actual data, but just this grouped data, could you still calculate the mean and standard deviation? Try the following: Pretend that each value in a bin lies exactly at the midpoint (i.e., 17 members stand 61 inches, 32 stand 64 inches, etc.). Now proceed exactly as you did before for the ungrouped data, and find the mean and standard deviation. Did you get good approximations to the actual values? Why do you think this method works as well as it does?

b) Write down a formula for the mean as you calculated it in part a), using “mi ” for midpoint of the ith bin and “fi ” for the frequency (count) of the i th bin. Do likewise for the variance.

Height Count 60-62 17 63-65 32 66-68 37 69-71 24 72-74 15 75-77 5