AP STATISTICS-UNIT 1
Hours of Sleep To gather data for a statistics project, a student asked 10 friends how many hours of sleep they got on the previous night. The data are shown in the following list. 7 6 5 9 3 4 7 9 5 8 What is the interquartile range (IQR) of the number of hours of sleep shown in the list? A) 3 hours B) 4 hours C) 6 hours D) 6.3 hours E) 6.5 hours
A: For the ordered set of data, the third quartile is 8 and the first quartile is 5. The IQR is the difference of 3.
Motel Occupancy The occupancy rate of a motel is the percentage of rooms that are occupied on a particular night. The histogram shown summarizes the occupancy rates for a random sample of 100 nights for a motel. Based on the histogram, which of the following best describes the shape of the distribution of occupancy rates? A) Skewed to the left B) Skewed to the right C) Symmetric D) Bimodal E) Uniform
B: The distribution of occupancy rates is skewed to the right because the right tail is longer than the left tail.
Car Price A reporter collected data on the purchase prices, in thousands of dollars, of 72 cars sold in a region. The following histogram summarizes the reporter's data. For a presentation on the data collected, the reporter used the median of the distribution to describe the typical purchase price. Which of the following might explain the use of median to describe the typical purchase price? A) There is an outlier between $80,000 and $85,000. Medians are resistant to outliers, while means are not. B) The number of observations that fall within a given interval is known. However, within each interval, the actual values are not known. C) The distribution is left skewed. D) The values represented in the histogram are in the thousands. E) The distribution is uniform.
A: Means are not resistant to outliers because their value is influenced by outliers. Medians are considered resistant because outliers do not greatly affect their value. The median better represents the typical purchase price.
Graduation Plans Just before graduation, a random sample of high school seniors were asked what their plans were for the coming year. A year after graduation, those same individuals were asked what their main activity was in the year since graduation. Their responses are shown in the following bar chart. Which of the following statements is supported by the bar chart? A) The percentage of students who selected Work as their main activity increased after graduation. B) The percentage of students who selected College as their main activity increased after graduation. C) Before graduation, there is no activity that greater than 50% of the students selected. D) Before graduation, the percentage of students who selected Tech School as their main activity was greater than the percentage who selected Work as their main activity. E) After graduation, the percentage of students who selected College as their main activity was twice the percentage of those who selected Work as their main activity.
A: The bars for Work increased from below 0.3 to above 0.3.
Tree Diameter The diameter, in centimeters (cm), of each tree in a random sample of trees in a forest was measured. The histogram shown summarizes the diameters. Which of the following is the best description of the distribution? A) The distribution consists of two clusters and a gap. B) The distribution is approximately normal. C) The distribution is symmetric with a skew to the right. D) The distribution is skewed to the left. E) The distribution is uniform.
A: The best description indicates the noticeable gap between 25 cm and 40 cm. A cluster is a concentration of data. Based on the histogram, there appears to be two clusters of data.
Favorite Subject Bar Chart A group of middle school students were asked which school subject was their favorite. The results are displayed by grade of student in the following bar chart. Which of the following statements is supported by the bar chart? A) For students who chose art, the number of grade 8 students was at least 100% greater than the number of grade 7 students. B) For students who chose social studies, the number of grade 8 students was at least 100% greater than the number of grade 7 students. C) For students who chose science, the number of grade 8 students was at least 50% less than the number of grade 7 students. D) For students who chose math, the number of grade 8 students was at least 50% less than the number of grade 7 students. E) For students who chose language arts, the number of grade 8 students was at least 100% greater than the number of grade 7 students.
A: The grade 7 bar extends to at most 8 students. A 100% increase would reach 16 students, and the grade 8 bar extends to at least 16 students.
Golf Strokes The following dot-plot shows the number of strokes taken by 20 professional golfers competing at an 18-hole golf course. Which of the following best describes the type of variable represented in the dot-plot? A) Quantitative and discrete B) Quantitative and continuous C) Categorical and discrete D) Categorical and continuous E) Quantitative and categorical
A: The number of strokes is a whole number.
Relative Humidity Relative humidity is a measure, expressed as a percentage, of the amount of water vapor present in air. The following histogram summarizes the relative humidity, at noon, for a random sample of 100 days for a certain city. Based on the histogram, which of the following is the best description of the distribution? A) The distribution displays a gap with a potential outlier located between 40% and 45%. B) The distribution displays a gap with potential outliers located between 90% and 95%. C) The distribution displays a gap with potential outliers located between 70% and 75%. D) The distribution displays two clusters with no apparent outliers. E) The distribution is uniform.
A: There are no observed data values between 45% relative humidity and 55% relative humidity, so there is a gap displayed in the distribution. The value located between 40% and 45% is unusually small when compared with the other data values. The value is a potential outlier; to test that it is an outlier would require using the 1.5×IQR rule or using the two standard deviations rule.
Cat Weight A family has two cats named Gordo and Flaco. Gordo weighs 15 pounds and Flaco weighs 8 pounds. A cat's weight is classified as unhealthy if the weight is located in the top 5% or bottom 5% of all cat weights. The distribution of cat weights is approximately normal with mean 9.5 pounds and standard deviation 1.5 pounds. Which of the following is the best description of Gordo's and Flaco's weights? A) Neither Gordo's nor Flaco's weight is classified as unhealthy. B) Gordo's weight is classified as unhealthy but Flaco's weight is not. C) Flaco's weight is classified as unhealthy but Gordo's weight is not. D) Flaco's weight and Gordo's weight are both classified as unhealthy. E) The classification of weight cannot be determined without more information.
B: Because Gordo's weight is over 3 standard deviations above the mean, his weight is in the top 5% of all weights and is classified as unhealthy. Flaco's weight is less than 2 standard deviations below the mean, so his weight is not in the bottom 5% of all weights and is not classified as unhealthy.
August Temperatures In the Dominican Republic in August, the distribution of daily high temperature is approximately normal with mean 86 degrees Fahrenheit (°F). Approximately 95% of all daily high temperatures are between 83°F and 89°F. What is the standard deviation of the distribution? A) 1°F B) 1.5°F C) 2°F D) 3°F E) 6°F
B: The empirical rule states that approximately 95% of the observations in a data set that is approximated by a normal curve will lie within 2 standard deviations of the mean. Since 95% of all daily high temperatures are between 83°F and 89°F, the interval from 83°F to 89°F has a width of 4 standard deviations (2 above the mean and 2 below the mean). So 1 standard deviation is 89−83/4°F=1.5°F.
Normal Models Which of the following can be reasonably modeled by a normal distribution? A) The favorite colors of students in a kindergarten class B) The heights of tomato plants that were all planted on the same day C) The percent of employees from a company who attended a company retreat D) The average number of siblings of all students at a particular high school E) The parental guidance ratings (G, PG, PG-13, R) of movies filmed in 2019
B: The heights of plants is a numeric and continuous variable, with a distribution that is typically symmetrically grouped around the mean with very few heights that are much larger or smaller than the mean.
Soccer Goals The following list shows the number of goals scored by a soccer team in each of 9 games. 0 0 1 1 1 3 3 4 5 How does the median number of goals scored compare with the mean number of goals scored? A) The median is equal to the mean. B) The median is less than the mean by 1. C) The median is greater than the mean by 1. D) The median is less than the mean by 2. E) The median is greater than the mean by 2.
B: The median is the middle value of a data set when the data are ordered. The median is the fifth value of the ordered data set, which is equal to 1. The mean is the sum of all data values divided by the number of values, which is equal to 2. The median is less than the mean by 1.
Favorite Color A group of first-grade students were asked to name their favorite color. The responses are shown in the following frequency table. Color Frequency Red 15 Blue 30 Green 8 Yellow 12 Purple 25 Which of the following statements is supported by the frequency table? A) More students chose purple than any other color. B) Twice as many students chose blue as chose red. C) Yellow was chosen by the least number of students. D) The total number of student responses is 80. E) The combined number of students who chose green and yellow is greater than the number of students who chose purple.
B: The number of students who chose red is 15, and 30 students chose blue. Since 30 is twice 15, the statement "Twice as many students chose blue as chose red" is supported by the data in the table.
Team Wins The following bar chart shows the number of wins for four middle-school basketball teams. Each team played 12 games. Which of the following statements is not supported by the bar chart? A) Team A won 75% of its games. B) Team B won 60% of its games. C) Team C won 7 games. D) Team D won less than half its games. E) Team C won 2 fewer games than Team A.
B: The statement is not supported by the bar chart. Team B won 6 games, and 6 out of 12 is 50%, not 60%.
Hiker Mean The following table shows the number of miles a hiker walked on a trail each day for 6 days. Day 1 2 3 4 5 6 Number of Miles 8 5 7 2 9 8 What was the mean number of miles the hiker walked for the 6 days? A) 3.5 B) 4.5 C) 6.5 D) 7.5 E) 8
C: The mean number of miles is the sum of the number of miles divided by the number of values. The sum of the number of miles is 8+5+7+2+9+8=39. The sum of the miles divided by the number of values is 39/6=6.5 miles.
Track Team Stats Which of the following variables for data about a track team is a discrete variable? A) The height of a team member B) The weight of a team member C) The number of times that a team member finished first in a race D) The time recorded for the last race that was run by a team member E) The time recorded for a one-mile race by a team member
C: The number of times that a team member finished first in a race is a count and is a discrete number.
Catfish Population Researchers studying catfish estimated the number of fingerling catfish and large catfish living in different rivers throughout the country. The following histograms summarize the relative frequency for each type of catfish. Based on the histograms, which of the following is the best comparison of the means and the ranges for the two distributions? A) The mean and range of the fingerling catfish are both equal to those of the large catfish. B) The mean and range of the fingerling catfish are both less than those of the large catfish. C) The mean and range of the fingerling catfish are both greater than those of the large catfish. D) The mean of the fingerling catfish is equal to that of the large catfish, and the range of the fingerling catfish is greater than that of the large catfish. E) The mean of the fingerling catfish is equal to that of the large catfish, and the range of the fingerling catfish is less than that of the large catfish.
C: The range of the distribution of fingerling catfish is between 6,000 and 8,000, while the range of the distribution of large catfish is between 1,500 and 2,000. Therefore the range of the distribution of fingerling catfish is greater than the range of the distribution of large catfish. The least value in the distribution of fingerling catfish is more than the greatest value of the distribution of large catfish. Therefore the mean of the distribution of fingerling catfish must be greater than the mean of the distribution of large catfish.
Convenience Store Purchase The distribution of the amount of a customer's purchase at a convenience store is approximately normal, with mean $15.50 and standard deviation $1.72. Which of the following is closest to the proportion of customer purchase amounts between $14.00 and $16.00 ? A) 0.19 B) 0.39 C) 0.42 D) 0.61 E) 0.81
C: The z-score associated with a purchase amount of $14.00 is z=14−15.5/1.72≈−0.872, and the z-score associated with a purchase amount of $16.00 is z=16−15.5/1.72≈0.291. The area under the standard normal curve between −0.872 and 0.291 is approximately 0.42, so this is the approximate proportion of customer purchase amounts between $14.00 and $16.00.
Puzzle Time The time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list. 9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58 One of the students who completed the puzzle claimed that there were two outliers in the data set. Based on the 1.5×IQR rule for outliers, is there evidence to support the student's claim? A) Yes, there are two outliers. One outlier is 9 minutes and the other outlier is 58 minutes. B) No, there is only one outlier at 9 minutes. C) No, there is only one outlier at 58 minutes. D) No, there are three outliers. One outlier is 9 minutes, one outlier is 35 minutes, and one outlier is 58 minutes. E) No, there are no outliers.
C: There is one outlier, 58, since it is more than 1.5 IQRs above the upper quartile (Q3), and all other data values are within 1.5 IQRs of either the first (Q1) or third quartile (Q3).
Presidential Variable The following table shows data collected about the thirty-third through fortieth presidents of the United States. All variables reported in the table are categorical. Name Political Party Eye Color Age at Inauguration Dominant Hand Harry S. Truman: Democrat Blue Typical Left Dwight D. Eisenhower: Republican Blue Typical Right John F. Kennedy: Democrat Blue Typical Right Lyndon B. Johnson: Democrat Brown Typical Right Richard Nixon: Republican Brown Typical Right Gerald Ford: Republican Blue Typical Both Jimmy Carter: Democrat Hazel Younger Right Ronald Reagan: Republican Blue Older Left Which of the variables in the table could have been reported differently such that the variable would be classified as quantitative? A) Name B) Political Party C) Eye color D) Age at inauguration E) Dominant hand
D: Age at inauguration could have been measured as a number of years
Movie Earnings The following boxplot summarizes the earnings made on one day at 45 movie theaters. Which of the following best compares the median movie theater earnings with the mean movie theater earnings? A) The median and mean are equal because the distribution is likely symmetric. B) The median and mean are equal because the distribution is likely skewed to the right. C) The median is less than the mean because the distribution is likely symmetric. D) The median is less than the mean because the distribution is likely skewed to the right. E) The median is less than the mean because the distribution is likely skewed to the left.
D: Although complete shape information cannot be determined from a boxplot, the position of the outliers and quartiles appears to indicate the distribution is skewed to the right. In a distribution that is skewed to the right, the median is likely less than the mean.
Moth Trap The distribution of the number of moths captured per night by a certain moth trap is approximately normal with mean 103. If 28 percent of the captures fall below 76 per night, which of the following equations can be used to find σ, the standard deviation of the distribution? A) 0.28 = 103−76/σ B) 0.28 = 76−103/σ C) −0.58 = 103−76/σ D) −0.58 = 76−103/σ E) 0.58 = 76−103/σ
D: Approximately 28% of the area under the standard normal curve is below a z-score of −0.58. Therefore −0.58=76−103/σ, and solving for σσ yields σ≈46.5 moths.
Construction Workers The following table shows summary statistics, in thousands, for the number of electrical workers and the number of concrete workers in the construction industry each month for the past 5 years. Type of Worker Minimum First Quartile Median Third Quartile Maximum Electrical 239 278 307 320 330 Concrete 186 262 290 308 335 Based on the 1.5×IQR rule for outliers, which of the following statements is a correct comparison of the two distributions? A) The electrical and concrete distributions both have high outliers. B) The electrical and concrete distributions both have lower outliers. C) Neither the electrical distribution nor concrete distribution has outliers. D) The concrete distribution has at least one lower outlier, and the electrical distribution has no lower outliers. E) The concrete distribution has at least one high outlier, and the electrical distribution has no high outliers.
D: For the concrete distribution, the minimum of 186 is less than the lower bound of 193. For the electrical distribution, the minimum of 239 is not less than the lower bound of 215.
Company Salaries The distribution of 27 salaries at a small company has mean $35,000 and standard deviation $2,000. Suppose the company hires a 28th employee at a salary of $120,000. Which of the following claims about the new salary distribution is supported? I. The median is not likely to change. II. The range is not likely to change. III. The mean is likely to increase. A) I only B) III only C) I and II only D) I and III only E) I, II, and III
D: Statement III (the mean is likely to increase) is correct, because means are not resistant to outliers. However, statement I (the median is not likely to change) is also correct, because medians are resistant to outliers.
Biking Club The following boxplot summarizes the heights of a group of people who participate in a weekend biking club. Which of the following statements is supported by the boxplot? A) The mean height is 67 inches. B) The number of people with height at least 70 inches is greater than the number of people with height at most 62 inches. C) The number of people with height at least 67 inches is less than the number of people with height at most 67 inches. D) Approximately 50% of the people have a height between 62 inches and 70 inches. E) Approximately 25% of the people have a height greater than 62 inches.
D: The interquartile range accounts for about 50% of the data. The first quartile is located at 62 and the third quartile is located at 70. Therefore approximately 50% of the people have a height between 62 inches and 70 inches.
Gas Prices The following bar chart shows the average price per gallon of gasoline for each month in 2004. Which of the following statements is not supported by the bar chart? A) The gas price was highest in June and October. B) The gas price increased each month from January through June. C) All months had gas prices greater than $1.50 per gallon. D) The gas price was lowest in February. E) The September gas price was higher than the January gas price.
D: The statement is not supported by the bar chart. January has the lowest bar in the bar chart, not February.
Absent From School The following relative frequency table shows reasons given by high school students for their last absence from school. Reason Relative Frequency Illness 0.57 Overslept 0.20 College visit 0.16 Did not finish assignment 0.07 Which of the following statements is not supported by the relative frequency table? A) More than half the students were absent because of illness. B) More than one-third of the students were absent because of oversleeping or college visits. C) The reason given the least number of times was did not finish assignment. D) Only 7 students were absent because they did not finish an assignment. E) Less than one-fourth of the students were absent because they overslept.
D: The statement is not supported by the relative frequency table. The proportion of students who gave a reason of did not finish assignment is 0.07, meaning that 7% of the total number of students, T, gave this reason. The number of students giving this reason is 0.07 T , but this number cannot be determined because T is not known.
Lecture Attendance The following table shows statistics on the ages, in years, of the people who attended a lecture last week. The data are summarized in the boxplot shown. N Mean St Dev Minimum Q1 Median Q3 Maximum 45 43 12 20 33 44 53 65 Which of the following statements is supported by the table and boxplot? A) The range of the distribution is 20 years. B) There were 43 people who attended the lecture. C) At least 50% of the people who attended the lecture were 43 years or younger. D) At least 75% of the people who attended the lecture were age 53 years or younger. E) At least 25% of the people who attended the lecture were 33 years old.
D: The third quartile, Q3, is 53. This indicates that at least 75% of the ages are at or below this value.
Ice Cream Variable A local ice-cream shop sells ice-cream cones for $2.00, and customers can choose from the following options. Ice-cream flavor Type of cone: sugar or waffle Chocolate dipped for an additional $0.50 Sprinkles for an additional $0.50 Which of the following is a quantitative variable? A) Ice-cream flavor B) Type of cone C) Chocolate dipped or not D) Sprinkles or not E) The total cost of the cone
E: A quantitative variable is one that takes on numerical values for a measured or counted quantity. The total cost of the cone is a quantitative variable since it can assume different numerical values representing the cost of each cone. The total cost of a cone could be $2.00 (ice cream in cone only), $2.50 (ice cream with sprinkles only or ice-cream cone with chocolate only), or $3.00 (ice-cream cone that is both chocolate dipped and has sprinkles).
College Variable Data are collected on the 35 students in a college history course. Which of the following is not a variable for the data set? A) Student birth month B) Political affiliation of student C) Student age D) Student address E) Number of students in the data set
E: A variable is a characteristic that can vary from student to student. The number of students in the data set is a single, fixed value (35).
Length of Engagement A sociologist studying marriage customs collected data on the length of time, in months, between the proposal and wedding. The following boxplot and table give the five-number summary for couples in which at least one person was getting married for the first time and for couples in which both people had been previously married. Period Minimum Q1 Median Q3 Maximum First Time 0.5 10 18 20 36 Previously Married 0.5 8 12 16 20 Based on the summary statistics, which of the following statements is supported by the boxplots and table? A) The mean length of time for first-time couples is 18 months, and the mean length of time for previously married couples is 12 months. B) There is a gap between 20 and 36 for the first-time married distribution. C) Because both distributions have a minimum of 0.5 months, the distributions are skewed to the left. D) The number of first-time couples in the study is greater than the number of previously married couples in the study. E) The interquartile range of length of time for first-time couples is greater than that of previously married couples.
E: The IQR (Q3 minus Q1) of length of time for first-time couples is 10 months (20 minus 10), while that of previously married couples is only 8 months (16 minus 8).
Bike Lanes Residents from five districts of a city were asked whether they were in favor of a city proposal to create new bike lanes in the roads. The following bar chart shows the relative frequency in each district of those who responded that they were in favor of the proposal. Which of the following statements is supported by the bar chart? A) District 2 has the greatest number of residents who are in favor of the proposal. B) District 1 has the least number of residents who are in favor of the proposal. C) All districts show at least 60% of residents in favor of the proposal. D) In 3 districts, less than half of the residents were in favor of the proposal. E) District 2 has the greatest percentage of residents who are in favor of the proposal.
E: The bars represent percentages, and District 2 has the highest bar (around 71%)
Traffic Flow The traffic engineer for a large city is conducting a study on traffic flow at a certain intersection near the city administration building. The engineer will collect data on different variables related to the intersection each day for ten days. Of the following variables, which will be measured using continuous data? A) The number of cars passing through the intersection in one hour B) The number of pedestrians crossing the intersection in one hour C) The number of bicyclists crossing the intersection in one hour D) The number of food trucks that park within four blocks of the intersection E) The number of minutes for a car to get from the intersection to the administration building
E: The number of minutes is a continuous variable. Between any two minutes, fractions of a minute can always be recorded
Middle School Activities The following table shows the numbers of students in grades 7 and 8 at a middle school who are participating in extracurricular activities. Band Chorus Chess Club Drama Club School Newspaper Grade 7: 15 22 8 16 10 Grade 8: 16 20 10 25 15 Which of the following statements is supported by the table? A) Each activity has more grade 8 students than grade 7 students. B) The number of students in Band is less than the number of students in the Chess Club. C) The total number of grade 7 students is greater than the total number of grade 8 students. D) The number of students in the Drama Club is more than twice the number of students in the School Newspaper. E) The activity with the greatest number of students is Chorus.
E: The total number of students in Chorus is 42, which is greater than the other totals.
Daily Bank Transactions The distribution of the number of transactions performed at a bank each day is approximately normal with mean 478 transactions and standard deviation 64 transactions. Which of the following is closest to the proportion of daily transactions greater than 350 ? A) 0.023 B) 0.046 C) 0.477 D) 0.954 E) 0.977
E: The value 0.977 is the total proportion of transactions that are greater than 350. The z-score associated with 350 transactions is −2. The proportion of daily transactions greater than 350 can be found using the z-score and technology, such as a calculator, a standard normal table, or computer-generated output.
Favorite Subject Students in a class were asked to choose their favorite school subject. The following frequency table summarizes the responses. School Subject Frequency Math 7 English 5 Science 4 Social Studies 2 Other 2 Which of the following statements is supported by the frequency table? A) More students chose math as their favorite subject than the combined number of students who chose English and science. B) Fewer students chose math as their favorite subject than the combined number of students who chose science and social studies. C) The total number of students in the class is less than 20. D) Seventy percent of the students chose math as their favorite subject. E) Less than half of the students chose math as their favorite subject.
E: Thirty-five percent of the students chose math as their favorite subject.
FR: Exploring Data- Campsite Exit Time and Children River Run campground has sites for people to use for camping. The sites can be reserved for a certain number of days. To help with cleaning and maintenance, the campground requests an exit time (the time at which campers leave the site) of 9 A.M. on the last day of the reservation. To estimate the typical exit time, the manager of River Run selected a random sample of 60 sites. Of the selected sites, 40 were reserved by people without young children, and 20 were reserved by people with young children. The following histograms summarize the exit times, recorded as minutes relative to 9 A.M.For example, an exit time of 9:30 A.M. is 30 minutes relative to an exit time of 9 A.M. Each interval contains possible values from the left endpoint up to but not including the right endpoint. (a) Consider the two histograms. (i) How many of the 60 sites had an exit time before 8:30 A.M.? (ii) How many of the 60 sites had an exit time of 11:00 A.M. or later? (b) Compare the distributions of the exit times for those without young children and those with young children. (c) Based on the histograms, what is a reasonable estimate of the median exit time for the random sample of 60 sites? Explain your reasoning.
a) (i) Three sites were vacated before 8:30 A.M. This is the sum of the counts represented by the two leftmost bars of the histogram of exit times for campsites without young children. No campers with small children vacated their campsites before 8:30 A.M. (ii) Eight sites were vacated at 11:00 A.M. or later. This is the sum of the counts represented by the two rightmost bars on each histogram. b) The distribution of exit times for campers without young children is skewed to the left while the distribution for campers with young children is roughly symmetric. Both exit time distributions appear to be unimodal. The distribution of exit times is more spread out for campers without young children; the largest possible range is around 210 minutes compared to a largest possible range of around 105 minutes for campers with young children. Campers without young children tend to leave the campground earlier than campers with young children; the median exit time for campers without young children is between 60 and 75 minutes after 9:00 A.M. which is less than the median exit time for campers with young children, which is between 90 and 105 minutes after 9:00 A.M. c) There are a total of 60 exit times, so the median falls between the 30th and 31st exit times. Since the 30th and 31st exit times fall between 10:15 and 10:30, any time between 10:15 A.M. and 10:30 A.M. provides a reasonable estimate of the median exit time.
FR: Comparing Distributions As a part of the United States Department of Agriculture's Super Dump cleanup efforts in the early 1990s, various sites in the country were targeted for cleanup. Three of the targeted sites—River X, River Y, and River Z—had become contaminated with pesticides because they were located near abandoned pesticide dump sites. Measurements of the concentration of aldrin (a commonly used pesticide) were taken at twenty randomly selected locations in each river near the dump sites. The boxplots shown below display the five-number summaries for the concentrations, in parts per million (ppm) of aldrin, for the twenty locations that were sampled in each of the three rivers. a) Compare the distributions of the concentration of aldrin among the three rivers. b) The twenty concentrations of aldrin for River X are given below. 3.4 4.0 5.6 3.7 8.0 5.5 5.3 4.2 4.3 7.3 8.6 5.1 8.7 4.6 7.5 5.3 8.2 4.7 4.8 4.6 Construct a stemplot that displays the concentrations of aldrin for River X. c) Describe a characteristic of the distribution of aldrin concentrations in River X that can be seen in the stemplot but cannot be seen in the boxplot.
a) Comparing the medians reveals that the concentration of aldrin tends to be highest for River X and lowest for River Z. About 50 percent of the concentrations of aldrin for Rivers X and Y are higher than all of the concentrations for River Z. River X also displays the most variability in aldrin concentrations, as seen by the largest range and largest IQR, and River Z has the least variability, as judged by both IQR and range. The shapes of the three distributions differ, in that the distribution appears to be skewed to the right for River X, roughly symmetric for River Y and slightly skewed to the left for River Z. b) Aldrin concentrations (in ppm) for River X Leaf unit = 0.1 (for example, 3 | 4 represents 3.4 ppm) 3 | 47 4 | 0236678 5 | 13356 6 | 7 | 35 8 | 0267 c) The stemplot shows a gap in the distribution of aldrin concentrations for River X between the values of 5.6 and 7.3 ppm of aldrin. This gap is not apparent in the boxplot.