Test 1C AP Statistics Name: Part 1: Multiple Choice. Circle the letter corresponding to the best answer. 1. At the beginning of the school year, a high-school teacher asks every student in her classes to fill out a survey that asks for their age, gender, the number of years they have lived at their current address, their favorite school subject, and whether they plan to go to college after high school. Which of the following best describes the variables that are being measured? (a) four quantitative variables (b) five quantitative variables (c) two categorical variables and two quantitative variables (d) two categorical variables and three quantitative variables (e) three categorical variables and two quantitative variables 2. The graph below shows how mothers of young children respond to the question, How many times a week do you choose fast food as a dining option for your family? 60 Percentage of responses 30 Never 1 3 times What s wrong with this method of presenting information? (a) This kind of data should always be presented in a pie chart. (b) The vertical axis should be number of responses, not percentage of responses. (c) The horizontal axis should be divided into more than three categories. (d) Using proportionally-sized hamburgers exaggerates differences between responses. (e) We don t know if the mothers who responded were thinking about dinner, or both lunch and dinner. 3. The median age of five people in a meeting is 30 years. One of the people a 50-year-old 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. 4 or more times
4. Below is a pie chart of how a randomly selected group of people described the cost of their health insurance. Which of the following bar graphs is equivalent to the pie chart? (a) (b) (c) (d) (e)
5. A researcher reports that the participants in his study lost a mean of 10.4 pounds after two months on his new diet. A friend of yours comments that she tried the diet for two months and lost no weight, so clearly the report was a fraud. Which of the following statements is correct? (a) Your friend must not have followed the diet correctly, since she did not lose weight. (b) Since your friend did not lose weight, the report must not be correct. (c) The report gives only the mean. This does not imply that all participants in the study lost 10.4 pounds or even that all lost weight. Your friend s experience does not necessarily contradict the study results. (d) In order for the study to be correct, we must now add your friend s results to those of the study and recalculate the new average. (e) Your friend is an outlier. 6. 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 Frequency Closing Price 7. 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 8. According to the U.S. Bureau of Labor Statistics, the monthly percentage change in the number of jobs in a certain state for the twelve months of 2011 had a mean of 0.08% and a standard deviation of 1.70%. From this information we can conclude that (a) The largest monthly change was 1.78% (b) The distribution of monthly changes is strongly skewed to the right. (c) Most of the monthly changes were negative. (d) The magnitude of the monthly deviations from the mean change averaged about 1.70%. (e) A mistake has been made. It makes no sense for the standard deviation to be greater than the mean.
9. The heights (in centimeters) of the male and female students in a class are summarized in the following boxplots: Which of the following is conclusions can be drawn from this graph?? (a) About 50% of the male students have heights between 170 and 178 centimeters. (b) About 25% of the male students are taller than the tallest female student. (c) The median height of male students is about 163 centimeters. (d) The mean height of male students is about 178 centimeters. (e) For female students, the mean height is lower than the median height. 10. 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. 11. 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.) (a) Describe the important features of this distribution. What does this tell you about how the econ (b) When asked for summary statistics, MINITAB produced the following output: Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Damage 50 22.39 3.60 25.45 0.00 2.23 12.66 41.63 88.60 Give the five-number summary, and explain why you can see from these five numbers that the distribution is strongly skewed to the right. (c) The histogram suggests that there may be outliers. Use the 1.5 x IQR rule of thumb to show that no values in this distribution meet this criterion for outliers.
12. Below are the lengths, in minutes, of the 25 most popular movies, as voted on by visitors to a web site devoted to movies. 142 195 201 139 106 175 96 121 130 109 200 133 102 178 165 161 124 146 115 118 154 152 207 112 136 (a) Make a stemplot of these data. (b) The mean of this distribution is 144.7 and the median is 139. Explain why you could have predicted that the mean would be higher than the median by looking at the stemplot. (c) The longest movie on the list, at 207 minutes, is Akira Kurosawa s classic The Seven Samurai. Suppose its place on the list was replaced by Andy Warhol s Sleep, which is 321 minutes of a man sleeping. Without performing any calculations, indicate whether each of the following measures of center and spread would increase, decrease, or remain the same. mean median standard deviation interquartile range
13. 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. Drive alone Car Pool Public transportation Male 113 16 6 Female 85 23 7 Discuss the relationship between gender and means of transportation to work for the working adults in this sample. Provide appropriate marginal and conditional distributions to support your answer. You may choose whatever methods you want to present those distributions. 14. Below are dotplots of three different distributions, A, B, and C. Which one has the largest standard deviation? Justify your answer.