Chapter 1 Review AP Statistics Part 1: Multiple Choice.
Name:
Circle the letter for your answer.
1. A reporter wishes to portray baseball players as overpaid. Which measure of center should he report as the average salary of major league players? (a) The mean. (b) The median. (c) The mode. (d) Either the mean or median. It doesn’t matter since they will be equal. (e) Neither the mean nor median. Both will be much lower than the actual average salary.
2.
A botanist is studying the petal lengths, measured in millimeters, of two species of lilies. The boxplots above illustrate the distribution of petal lengths from two samples of equal size, one from species A and the other from species B. Based on these boxplots, which of the following is a correct conclusion about the data collected in this study? (a) The interquartile ranges are the same for both samples. (b) The range for species B is greater than the range for species A. (c) There are more petal lengths that are greater than 70 mm for species A than there are for
species B. (d) There are more petal lengths that are greater than 40 mm for species B than there are for
species A. (e) There are more petal lengths that are less than 30 mm for species B than there are for
species A.
3. If the largest value of a data set is doubled, which of the following is not true? (a) The mean increases. (b) The standard deviation increases. (c) The interquartile range increases. (d) The variance increases. (e) The median remains unchanged.
4. A particularly common question in the study of wildlife behavior involves observing contests between “residents” of a particular area and “intruders.” In each contest, the “residents” either win or lose the encounter (assuming there are no ties). Observers might record several variables, listed below. Which of these variables is categorical? (a) The duration of the contest (in seconds) (b) The number of animals involved in the contest (c) Whether the “residents” win or lose (d) The total number of contests won by the “residents” (e) None of these
5. Fourth grade children were asked what emotion they associated with the color red. The responses for emotion and gender of the children are summarized in the following two-way table. Anger
Pain
Happiness
Love
Male
35
27
12
38
Female
27
17
19
39
What proportion of the males associate the color red with love? (a) (b) (c) (d) (e)
0.5234 0.3598 0.3393 0.1822 0.1775
6. A study was conducted to determine the effectiveness of varying amounts of vitamin C in reducing the number of common colds. A survey of 450 people provided the following information:
None 57 No colds At least one cold
223
Daily amount of Vitamin C taken 500 mg 26 84
1000 mg 17 43
What conclusion can be made? (a) The data proves that vitamin C reduces the number of common colds. (b) The data proves that vitamin C has no effect on the number of common colds. (c) There appears to be a strong association between consumption of vitamin C and the occurrence of common colds. (d) There appears to be little association between consumption of vitamin C and the occurrence of common colds. (e) Since common colds are caused by viruses, there is no reason to conclude that vitamin C could have any effect.
Part 2: Free Response Answer completely, but be concise. Write sequentially and show all steps. 7. If you were working with a skewed distribution, which numerical summary would you recommend, (1) the mean and standard deviation or (2) the five number summary? Explain.
8. 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 11 and 70?
9. The histogram at the right shows the number of hurricanes reaching the east coast of the United States each year over a 70-year period. a) Describe the shape of the distribution.
b) Which is higher, the mean or the median?
10. We all know that the body temperature of a healthy person is 98.6 °F. In reality, the actual body temperature of individuals varies. Here is a back-to-back stemplot of the body temperatures of 130 healthy individuals (65 males and 65 females). Leaf unit = 0.1 (a) Summary statistics for males and females are shown below. Median Min Max Q1 Q3 Males 98.1 96.3 99.5 97.6 98.6 Females 98.4 96.4 100.8 97.95 98.8 Use the summary statistics to determine whether any of the females are outliers. Justify your answer.
Males Females 3 96 96 4 7 96 7 9 96 8 1110 97 32 97 22 544444 97 4 7666 97 677 998888 97 8888999 11000000 98 000001 332222 98 222222333 554444 98 444445 77666666 98 6666777777 9888 98 8888889 1000 99 0011 32 99 223 54 99 4 99 99 9 100 0 100 100 100 100 8
(b) Write a few sentences comparing the body temperatures of adult males and females.
11. The table below describes the data comparing the relationship between age groups and localities of residence.
Localities of Residence
Age Groups
Urban
Suburban
Rural
Under 25
110
150
65
25-50
240
220
75
Over 50
53
112
58
Totals
Totals (a) Compute the marginal frequencies (in counts). Place the answers in the table. (b) Compute the marginal relative frequencies (percentages). Place answers below or on the side of the table.
(c) What percent of the suburban dwellers are over 50?
(d) What percent of the over-50 residents live in rural areas?
(e) Give the conditional distribution (in percentages) of age groups for the urban dwellers:
(f) Do you believe that these data indicate there is a relationship between locality of residence and the ages of the residences? Explain your answer using appropriate statistical evidence.
Chapter 1 Learning Targets: __ I can identify whether a variable is categorical or quantitative. __ I can explain what is meant by “distribution of a variable.” __ I can interpret (i.e. describe and answer questions about) pie charts. __ I can construct and interpret bar graphs, dotplots, stemplots, and histograms. __ I can make two-way tables and display their data in an appropriate graph. __ I can calculate marginal and conditional distributions and use the results to answer questions. __ I can use SOCS—shape (symmetric, skewed left or right, etc.), outliers, center (as measured by mean or median), spread (range, IQR, or st. dev.) – to describe distributions of quantitative data. __ I can explain the differences between mean and median and describe the strengths and weaknesses of each. __ I can calculate the quartiles and IQR of a distribution and describe their properties. __ I can apply the 1.5•IQR rule to determine whether a value in a distribution is an outlier. __ I can calculate the five-number summary of a distribution and explain the properties of the numbers in the five number summary. __ I can construct and interpret boxplots. __ I can explain what variance and standard deviation measure and describe their properties. __ I can explain what resistance is and explain why mean, median, IQR, standard deviation, etc. are or are not resistant. __ I can compare distributions using side-by-side (parallel) boxplots, side-by-side bar graphs, back-to-back stemplots, back-to-back dotplots, and back-to-back histograms. __ I can use SOCS to compare distributions, making sure to use comparative language in comparing the centers and spreads.
