AP Statistics @ Woodward Academy Tuesday, August 31, 2004 Coley / P. Myers Test #1 (Chapters 2-5) Name ______
Part I - Multiple Choice (Questions 1-6) - Circle the answer of your choice.
1. A large company has offices in two locations, one in New Jersey and one in Utah. The mean salary of the office assistants in the New Jersey office is $28,500. The mean salary of office assistants in the Utah office is $22,500. The New Jersey office has 128 office assistants and the Utah office has 32 office assistants. What is the mean salary paid to the office assistants in this company?
(a) $22,500 (b) $23,700 (c) $25,500 (d) $27,300 (e) $28,500
2. In the northern U.S., schools are sometimes closed during winter due to severe snowstorms. At the end of the school year, schools have to make up for the days missed. The following graph shows the frequency distribution of the number of days missed due to snowstorms per year, using data from the past 75 years. Bad Weather Histogram 18 16 14 12 t n
u 10 o
C 8 6 4 2
0 2 4 6 8 10 12 14 Days_Missed
Which of the following should be used to describe the center of the distribution?
(a) Mean, because it is always the best measure. (b) Median, because the distribution is skewed. (c) IQR, because it excludes outliers and includes only the middle 50 percent of the data. (d) First quartile, because the distribution is left skewed. (e) Standard deviation, because it is unaffected by outliers.
3. The stemplot displays the 1988 per capita income (in hundreds of dollars) of the 50 states. Which of the following best describes the data?
(a) Skewed distribution, mean greater than median (b) Skewed distribution, median greater than mean (c) Symmetric distribution, mean greater than median (d) Symmetric distribution, median greater than mean (e) Symmetric distribution with outliers on high end 4. A resident of Auto Town was interested in finding the cheapest gas prices at nearby gas stations. On randomly selected days over a period of one month, he recorded the gas prices (in dollars) at four gas stations near his house. The box plots of gas prices are as follows:
Which station has more consistent gas prices?
(a) Station 1 (b) Station 2 (c) Station 3 (d) Station 4 (e) Cannot be determined
5. A small kiosk at the Atlanta airport carries souvenirs in the price range of $3.99 to $29.99, with a mean price of $14.75. The airport authorities decide to increase the rent charged for a kiosk by 5 percent. To make up for the increased rent, the kiosk owner decides to increase the prices of all items by 50 cents. As a result, which of the following will happen?
(a) The mean price and the range of prices will increase by 50 cents. (b) The mean price will remain the same, but the range of prices will increase by 50 cents. (c) The mean price and the standard deviation of prices will increase by 50 cents. (d) The mean price will increase by 50 cents, but the standard deviation of prices will remain the same. (e) The mean price and the standard deviation of prices will stay the same.
6. Which of the following are true statements?
I. The standard deviation is the square root of the variance. II. The standard deviation is zero only when all values are the same. III. The standard deviation is strongly affected by outliers.
(a) I and II (b) I and III (c) II and III (d) I, II, and III (e) None of the above gives the complete set of true responses. Part II – Free Response (Questions 7-9) – Show your work and explain your results clearly.
7. The summary statistics for the number of inches of rainfall in Los Angeles for 117 years, beginning in 1877, are shown below.
N MEAN MEDIAN STDEV 117 14.941 13.070 6.747
MIN MAX Q1 Q3 4.850 38.180 9.680 19.250
(a) Describe a procedure that uses these summary statistics to determine whether there are outliers.
(b) Are there outliers in these data? Justify your answer based on the procedure that you described in part (a).
(c) The news media reported that in a particular year, there were only 10 inches of rainfall. Use the information provided to comment on this reported statement. 8. The table of data below provides the cumulative proportions for the United States population at selected ages for the years 1900 and 2000 (projected). For example, 0.344 or 34.4 percent of the population was at or under age 15 in 1900, while 0.209 or 20.9 percent will be at or under age 15 in the year 2000. The graph below shows the cumulative proportions plotted against age for the years 1900 and 2000 (projected). The data and graph are to be used to compare the age distributions for the year 1900 with the projected age distribution for the year 2000.
Age 1900 2000 1.0 1900 5 0.121 0.066 2000 n 0.8 o i 15 0.344 0.209 t r o p
o 0.6
25 0.540 0.344 r P
e v
35 0.700 0.480 i
t 0.4 a l 45 0.822 0.643 u m
u 0.2 55 0.906 0.781 C 0.0 65 0.959 0.870 5 15 25 35 45 55 65 Age
(a) Approximate the median age for each distribution.
(b) Approximate the interquartile range for each distribution.
(c) Using the results from parts (a) and (b), write a sentence or two for a history textbook comparing the age distributions for the years 1900 and 2000. 9. Five hundred randomly selected middle-aged men and five hundred randomly selected young adult men were rated on a scale of 1 to 10 on their physical flexibility, with 10 being the most flexible. Their ratings appear in the frequency table below. For example, 17 middle-aged men had a flexibility rating of 1.
Frequency of Frequency of Physical Flexibility Rating Middle-Aged Men Young Adult Men 1 17 4 2 31 17 3 49 29 4 71 39 5 70 54 6 87 69 7 78 83 8 54 93 9 34 73 10 9 39
(a) Display these data graphically so that the flexibility of middle-aged men and young adult men can be easily compared.
(b) Based on an examination of your graphical display, write a few sentences comparing the flexibility of middle-aged men with the flexibility of young adult men.