[EX02-195] Following are the percentage of high school graduates per state from the class of 2003 who took the ACT exam.

0.73 0.07 0.16 0.10 0.52 0.62 0.69 0.70 0.12 0.76 0.32 0.05 0.60 0.69 0.73 0.15 0.12 0.74 0.16 0.73 0.27 0.30 1.00 0.67 0.34 0.15 0.08 0.33 0.63 0.80 0.73 0.41 0.21 0.88 0.08 0.80 0.06 0.67 0.69 0.07 0.15 0.22 0.66 0.69 0.06 0.64 0.34 0.11 0.62 0.12 Source: ACT Inc., The College Board

a. Examine the data in the table. What shape distribution do you anticipate these data will produce?

Explain why you chose the shape distribution you did.

b. Construct the histogram of these percentages.

c. Describe, in detail, the distribution of your histogram in part b.

d. Compare your description in part c to your expectations in part

a. How close were you?

What did you not think about in part a that is apparent now that you see the actual distribution?

e. Find the mean percentage.

f. Where does the mean fall on the distribution?

Locate the mean on the histogram constructed for part

b. Is the mean percentage representative of these data? Explain.

g. Find the standard deviation.

h. On the histogram constructed for part

b, locate the values 1 standard deviation above and below the mean. How much of the distribution is between these values?

i. Why is the standard deviation so large? Explain in detail.