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# Confidence Interval

DESCRIPTIVE STATISTICS

i. ▪ Both graphs have a single peak.

▪ Both graphs display 6 class intervals.

▪ Both graphs show the same general pattern.

ii. Answers may vary. Possible answers include: Although the width of the class intervals for couples is double that of the class intervals for singles, the graphs are more similar than they are different.

g. Answers may vary. Possible answers include: You are able to compare the graphs interval by interval. It is easier to compare the overall patterns with the new scale on the Couples graph. Because a couple represents two individuals, the new scale leads to a more accurate comparison.

h. Answers may vary. Possible answers include: Based on the histograms, it seems that spending does not vary much from singles to individuals who are part of a couple. The overall patterns are the same. The range of spending for couples is approximately double the range for individuals.

79 c

83 a. 1 – (0.02+0.09+0.19+0.26+0.18+0.17+0.02+0.01) = 0.06

b. 0.19+0.26+0.18 = 0.63

c. Check student’s solution.

d. 40th percentile will fall between 30,000 and 40,000

80th percentile will fall between 50,000 and 75,000

e. Check student’s solution.

85 a. more children; the left whisker shows that 25% of the population are children 17 and younger. The right whisker shows

that 25% of the population are adults 50 and older, so adults 65 and over represent less than 25%.

b. 62.4%

87 a. Answers will vary. Possible answer: State University conducted a survey to see how involved its students are in

community service. The box plot shows the number of community service hours logged by participants over the past year.

b. Because the first and second quartiles are close, the data in this quarter is very similar. There is not much variation in the values. The data in the third quarter is much more variable, or spread out. This is clear because the second quartile is so far away from the third quartile.

89 a. Each box plot is spread out more in the greater values. Each plot is skewed to the right, so the ages of the top 50% of

buyers are more variable than the ages of the lower 50%.

b. The BMW 3 series is most likely to have an outlier. It has the longest whisker.

c. Comparing the median ages, younger people tend to buy the BMW 3 series, while older people tend to buy the BMW 7 series. However, this is not a rule, because there is so much variability in each data set.

d. The second quarter has the smallest spread. There seems to be only a three-year difference between the first quartile and the median.

e. The third quarter has the largest spread. There seems to be approximately a 14-year difference between the median and the third quartile.

f. IQR ~ 17 years

g. There is not enough information to tell. Each interval lies within a quarter, so we cannot tell exactly where the data in that quarter is concentrated.