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# In Exercise 4.5, you were asked to depict graphically the distribution of the following sample of statistics exam completion times (in minutes):

In Exercise 4.5, you were asked to depict

graphically the distribution of the following

sample of statistics exam completion times

(in minutes):

61 86 61 58 70 75 66 77 66 64

73 91 65 59 86 82 48 67 55 77

80 58 94 78 62 79 83 54 52 45

Find the mean and the median of this set of

completion times.

b Using the frequency distribution in Exercise

4.5, determine the mode as the midpoint of

the modal class.

c Locate the mean, the median and the

mode on the relative frequency histogram

constructed in Exercise 4.5.

d Use the shortcut formula to find the variance

of this sample of completion times.

why short cut formula is different？， can you explain this part？

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