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Additional Questions Test 1: Exploring Data AP Statistics

Name:

Directions: Work on these sheets. Answer completely, but be concise.

Part 1: Multiple Choice. Circle the letter corresponding to the best answer.

1. The median age of five people in a meeting is 30 years. One of the people, whose age is 50 years, leaves the room. The median age of the remaining four people in the room is

(a) 40 years.

(b) 30 years.

(c) 25 years.

(d) less than 30 years.

(e) Cannot be determined from the information given.

2. Below is a pie chart of how a randomly selected group of people described the cost of their heath insurance.

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Which of the following bar graphs is equivalent to the pie chart?

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3. A small company estimating its photocopying expenses finds that the mean number of copies made per day for the past 12 months is 258 copies per day with a standard deviation of 24 copies per day. Which of the following is a correct interpretation of standard deviation?

(a) The number of copies made per day was always between 234 and 282.

(b) About 95% of the time, the number of copies made per day was between 234 and 282.

(c) The difference between the mean number of copies made per day and the median number of copies made per day was 24.

(d) On average, the number of copies made each day was about 24 copies per day away from the mean, 258.

(e) 1.5 times the interquartile range of copies made per day is 24.

4. The five-number summary for scores on a statistics exam is 11, 35, 61, 70, 79. In all, 380 students took the test. About how many had scores between 35 and 61?

(a) 26

(b) 76

(c) 95

(d) 190

(e) None of these

5. The following is a histogram showing the actual frequency of the closing prices of a particular stock on the New York Stock Exchange over a 50-day period. The class that contains the third quartile is

(a) 10–20

(b) 20–30

(c) 30–40

(d) 40–50

(e) 50–60

6. For the data in the previous problem, which measures of center and spread would be most appropriate to use?

(a) Mean and standard deviation

(b) Mean and interquartile range

(c) Mean and range

(d) Median and interquartile range

(e) Median and standard deviation

7. The weights of the male and female students in a class are summarized in the following boxplots:

Which of the following is NOT correct?

(a) About 50% of the male students have weights between 150 and 185 pounds.

(b) About 25% of female students have weights above 130 pounds.

(c) The median weight of male students is about 162 pounds.

(d) The mean weight of female students is about 120 pounds.

(e) The male students have less variability than the female students.

8. When testing water for chemical impurities, results are often reported as bdl, that is, below detection limit. The following are the measurements of the amount of lead in a series of water samples taken from inner-city households (in parts per million):

5, 7, 12, bdl, 10, 8, bdl, 20, 6

Which of the following statements can we be sure is true?

(a) The mean lead level in the water is about 10 ppm.

(b) The mean lead level in the water is about 9 ppm.

(c) The median lead level in the water is 7 ppm.

(d) The median lead level in the water is 8 ppm.

(e) Neither the mean nor the median can be computed because some values are unknown.

Part 2: Free Response

Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

The states differ greatly in the kinds of severe weather that afflict them. The histogram below shows the distribution of average annual property damage caused by tornadoes over the period from 1950 to 1999 in the 50 United States. (To adjust for the changing buying power of the dollar over time, all damages were restated in 1999 dollars.)

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9. Describe the important features of this distribution. What does this tell you about how the economic burden of tornados is distributed among the states?

10. When asked for summary statistics, MINITAB produced the following output:

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Given the statistics above, explain why you can see from these numbers that the distribution is strongly skewed to the right.

11. The histogram suggests that there may be outliers. Use the 1.5 x IQR rule to show that no values in this distribution meet this criterion for outliers.

12. The two-way table below shows the relationship between means of transportation to work and gender for a simple random sample of 250 working adults in the United States.

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Calculate the conditional distributions for means of transportation to work for each gender.

Discuss the relationship between gender and means of transportation to work for the working adults in this sample.

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