stats unit one review (final)
The following list shows the selling prices of 8 houses in a certain town. HousePriceHousePriceA$302,100E$275,800B$275,800F$295,000C$305,400G$281,900D$250,600H$284,700 What is the median selling price of the houses in the list?
$283,300
Of the following dotplots, which represents the set of data that has the greatest standard deviation?
0, 10; only on the far sides
The number of hurricanes reaching the East Coast of the United States was recorded for each of the last ten decades by the National Hurricane Center. Summary measures are shown below. Min = 12 Max = 24 Lower quartile = 15 Upper quartile = 18 Median = 16 n = 10 Which of the following statements is true?
24 is an outlier and it is possible that there are other outliers at the high end of the data set. There are no outliers at the low end of the data set.
The following question(s) refer to the following scenario and set of data. In the 1830s, land surveyors began to survey the land acquired in the Louisiana Purchase. Part of their task was to note the sizes of trees they encountered in their surveying. The table of data below is for bur oak trees measured during the survey. An outlier may be defined as a data point that is more than 1.5 times the interquartile range below the lower quartile or is more than 1.5 times the interquartile range above the upper quartile. According to this definition, what is the diameter, in inches, of the smallest tree that is an outlier?
34
The histogram below displays the frequencies of waiting times, in minutes, for 175 patients in a dentist's office. Which of the following could be the median of the waiting times, in minutes?
7.25
The dotplot below displays the total number of miles that the 28 residents of one street in a certain community traveled to work in one five-day workweek. Which of the following is closest to the percentile rank of a resident from this street who traveled 85 miles to work that week?
70
A random sample of 25 households from the Mountainview School District was surveyed. In this survey, data were collected on the age of the youngest child living in each household. The histogram below displays the data collected in the survey. In which of the following intervals is the median of these data located?
8 years old to less than 10 years old
Researchers conducted a telephone survey of 427 adults living in a large city. The adults were asked whether they planned to purchase a smart watch in the next year. The table shows the responses categorized by the region of the city in which the residents live. Which of the following graphical displays is most appropriate for comparing the proportions of those surveyed who plan to purchase a smart watch within the four regions?
A segmented bar chart
Professor James gave the same test to his three sections of statistics students. On the 35-question test, the highest score was 32 and the lowest was 15. Based on the information displayed in the boxplots above, which of the following statements is true?
At least 50% of the scores in section 3 are higher than all of the scores in section 1.
Data were collected on the amount, in dollars, that individual customers spent on dinner in an Italian restaurant. The quartiles for these data are given below. Which of the following statements must be true for these customers?
At least half of the customers spent less than or equal to $44.27 and at least half spent greater than or equal to $44.27.
The following bar chart shows the relative frequency of days of rain for 30 days in four regions of a certain state. Which of the following statements is not supported by the bar chart?
Region C had more than 25 days of rain.
Athletes in a particular sport are classified as either offense or defense. The distribution of weights for the athletes classified as offense is approximately normal, centered at 200 pounds, and ranges from 150 pounds to 250 pounds. The distribution of weights for the athletes classified as defense is approximately normal, centered at 300 pounds, and ranges from 250 pounds to 350 pounds. There are 1,000 athletes in each classification. Which of the following is the best description of a histogram of the weights of all 2,000 athletes?
Bimodal
The following table shows the data collected from students in grades 3 and 4 in an elementary school about their favorite types of pets. CatsDogsBirdsOtherTotalGrade 32560515105Grade 435501510110Total601102025215 Which of the following statements is supported by the table?
Dogs were the type of pet chosen most often by the students at the elementary school.
Three brands of candy pieces—X, Y, and Z—are made in many colors. Shaela bought one bag of each brand and counted the number of pieces of each color. The graph below shows the relative frequency distribution of colors for each bag. Which of the following statements must be true?
For Brand Y, there were more red candy pieces than green candy pieces in the bag.
As part of a community service program, students in three middle school grades (grade 6, grade 7, grade 8) each chose to participate in one of three school-sponsored volunteer activities. The graph below shows the distribution for each class for the three activities. Based on the graph, which statement must be true?
For students in grade 7, the number who chose activity C was greater than the number who chose activity B.
The following pie chart summarizes the results of a survey given to airlines about the primary reason for flight delays. Which of the following statements is supported by the pie chart?
More delays were caused by weather than by all other reasons combined.
Roger claims that the two statistics most likely to change greatly when an outlier is added to a small data set are the mean and the median. Is Roger's claim correct?
No, only the mean is likely to change greatly
The following frequency table shows the responses from a group of college students who were asked to choose their favorite flavor of ice cream. FlavorFrequencyVanilla100Chocolate65Strawberry35Mint chip45Coffee30Butter pecan25 Which of the following statements is not supported by the table?
One-half of the students chose vanilla or chocolate.
The following list shows the number of video games sold at a game store each day for one week. 15, 43, 50, 39, 22, 16, 20 Which of the following is the best classification of the data in the list?
Quantitative and discrete
A veterinarian collected data on the weights of 1,000 cats and dogs treated at a veterinary clinic. The weight of each animal was classified as either healthy, underweight, or overweight. The data are summarized in the table. Based on the data in the table, which of the following is the most appropriate type of graph to visually show whether a relationship exists between the type of animal and the weight classification?
Segmented bar chart
The prices, in thousands of dollars, of the 35 used cars at a certain car dealership are shown in the table below. Which of the following best describes the shape of the distribution of used car prices at the dealership?
Skewed to the right (positively skewed)
A certain motel is roughly 20 miles from the entrance to Yosemite National Park. The motel manager wants to get a better estimate of the distance and asks five people to each measure the distance, to the nearest tenth of a mile, using the odometer in his or her car. The manager will use the median of the five measurements as the estimate of the distance. Which of the following statements is NOT a statistical justification for the manager's plan?
The actual distance should be considered a variable, and taking five measurements allows the manager to estimate the variability in the actual distance.
The following table summarizes the number of pies sold at a booth one day at a local farmers market. Type of PieFrequencyApple18Blueberry14Cherry16Key Lime12Peach12Pumpkin18 Which of the following statements is supported by the table?
The combined percentage of key lime pies sold and pumpkin pies sold was less than 50%.
Which of the following describes a continuous variable?
The diameters of the tree trunks at an evergreen farm
An airline recorded the number of on-time arrivals for a sample of 100 flights each day. The boxplot below summarizes the recorded data for one year. Based on the boxplot, which of the following statements must be true?
The difference between the median and the lower quartile for the number of on-time arrivals is less than 2.
Which of the following statements is true about a distribution that appears to have a gap when displayed as a histogram?
The distribution has a region between two data values where no data were observed.
The following dotplot shows the scores of 25 people who played an online trivia game. Which of the following statements is the best description of the distribution of scores?
The distribution is skewed right.
New employees at a large corporation go through a training program during their first week of employment. The new employees take a written assessment at the completion of the program to determine how well prepared they are for their jobs. A score greater than the mean indicates a well-prepared employee. Assume the following distributions of new employee scores have the same mean score, the same maximum score, and the same minimum score. Which distribution has a shape that is most likely to represent the greatest percent of well-prepared employees?
The distribution of scores is skewed to the left.
Each person in a random sample of adults was asked how many DVDs he or she owned. Summary statistics are given below. Which of the following statements is true?
The interquartile range of the number of DVDs owned is 65.
The following histogram shows the ages, in years, of the people who attended a documentary at a movie theater. Based on the histogram, which of the following statements best describes the relationship between the mean and the median of the distribution of ages?
The mean is most likely less than the median because the distribution is skewed to the left.
Which of the following statistics is defined as the 50th percentile?
The median
The figure above summarizes the heights, in centimeters, of approximately 400 pine seedlings six years after they were planted at a center for environmental study. Approximately half of the trees were fertilized yearly, and the remaining trees were never fertilized. Which of the following statements about the medians and interquartile ranges (IQRs) of the heights of the two groups of trees 6 years after being planted is true?
The median for the unfertilized trees is less than the median for the fertilized trees, and the IQR is greater for the unfertilized trees.
The number of siblings was recorded for each student of a group of 80 students. Some summary statistics and a histogram displaying the results are shown below. An outlier is often defined as a number that is more than 1.5 times the interquartile range below the first quartile or above the third quartile. Using the definition of an outlier and the given information, which of the following can be concluded?
The median is less than the mean, and the distribution has two outliers.
The prices, in thousands of dollars, of 304 homes recently sold in a city are summarized in the histogram below. Based on the histogram, which of the following statements must be true?
The median price is not greater than $750,000.
Data will be collected on the following variables. Which variable can be considered discrete?
The number of books a person finished reading last month
The following segmented bar chart shows the number of flights that were either on time or delayed at three different airports on one day. Which of the following statements is supported by the bar chart?
The number of on-time flights at Airport S is half the number of on-time flights at Airport T.
The following relative frequency table shows the political party affiliation for a sample of 500 people in a certain town. Political PartyRelative FrequencyDemocrat0.35Republican0.30Independent0.20Green Party0.11Libertarian0.03Other0.01 Which of the following statements is supported by the table?
The number of people affiliated with the Independents is 100.
The following bar chart displays the relative frequency of responses of students, by grade level, when asked, "Do you volunteer in a community-service activity?" Which of the following statements is not supported by the bar chart?
The number of tenth-grade students who responded yes was greater than the number of ninth-grade students who responded yes.
A child psychologist asked 100 five year olds and 50 ten year olds to name their favorite color. Their results are shown in the following table. RedOrangeYellowGreenBluePurpleFive year olds21158103511Ten year olds72615128 Which of the following statements is supported by the table?
The percentage of five year olds who selected red or blue as their favorite color is greater than the percentage of ten year olds who selected red or blue as their favorite color.
Grain moisture is a characteristic of grain that affects the price paid for the grain. A random sample of 28 loads of corn was evaluated for moisture as a percent of the total weight. A different random sample of 28 loads of soybeans was also evaluated for moisture. The data are displayed in the dotplots below. Based on the dotplots, which of the following is greater for the percent moisture of corn than for the percent moisture of soybeans?
The range
The following table shows summary statistics for the number of hours a group of students spent playing video games last Monday and last Saturday. DayMinimumQ1MedianQ3MaximumMonday012412Saturday146818 Based on the summary statistics, which of the following gives the best comparison of the range and the interquartile range (IQR) of the two days?
The range and IQR of hours played on Monday are both less than the range and IQR of hours played on Saturday.
A data set of test scores is being transformed by applying the following rule to each of the raw scores. Transformed score = 3.5(raw score) + 6.2 Which of the following is NOT true?
The range of the transformed scores equals 3.5(the range of the raw scores) + 6.2.
The following histogram summarizes the amount spent on plane tickets to travel home, in dollars, for a group of 30 college students. If the interval size is decreased from $200 to $100, which of the following must remain the same on the new histogram?
The sum of the frequencies
A graph (not shown) of the selling prices of homes in a certain city for the month of April reveals that the distribution is skewed to the left. Which of the following statements is the most reasonable conclusion about the selling prices based on the graph?
The value of maximum minus third quartile is less than the value of first quartile minus minimum.
Data were collected on 100 United States coins minted in 2018. Which of the following represents a quantitative variable for the data collected?
The value of the coin
The following table shows data for the 8 longest roller coasters in the world as of 2015. Length (feet)TypeSpeed (miles per hour)Height (feet)Drop (feet)Continent8,133Steel95318310Asia7,442Steel50107102Europe7,359Wood65110135North America6,709Steel81259230Asia6,602Steel95325320North America6,595Steel93310300North America6,562Steel149171168Asia6,442Wood67163154North America Which of the following variables is categorical?
Type
Which of the following questions about cars in a school parking lot will allow for the collection of a set of categorical data?
What are the colors of the cars in the lot?
Administrators at a state university computed the mean GPA (grade point average) for juniors and seniors majoring in either physics or chemistry. The results are displayed in the table below. When juniors and seniors are grouped together, could physics majors have a higher mean GPA than chemistry majors?
Yes. It could happen. Whether it does happen depends on the number of juniors and seniors in each major.
For which of the following distributions is the mean greater than the median?
slopes to the left