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Data Displays and Statistics Answers

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1
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What is the best definition for “sample” as used in statistics?

A
the entire population of the group
B
a part of the population that represents the entire population
C
the difference between the maximum and minimum values observed
D
a measure of how much the values within a population vary
2
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Which type of graph most readily shows the interquartile range for a data set?

A
bar graphs
B
box plots
C
dot plots
D
histograms
3

Which data collections show bias? Check all that apply.

A
An English teacher polls the top-ten most avid readers to find their favorite books.
B
An insurance company polls drivers of sports cars to find their average number of tickets.
C
A restaurant manager surveys every tenth customer for one week.
D
An assistant principal surveys each student who is sent for discipline.
E
A fundraiser organizer draws five names from a hat that contains all entries.
4

Which dot plot shows a sample that is most representative of the number of pets in a household?

A
A dot plot going from 0 to 6. There are 3 dots above 0, 5 dots above 1, 4 dots above 2, 3 dots above 3, 2 dots above 4, 0 dots above 5, and 1 dot above 6.
Option A
B
A dot plot going from 0 to 6. There are 2 dots above 1, 3 dots above 2, and 1 dot above 5.
Option B
C
A dot plot going from 0 to 6. There is 1 dot above 0, 2 dots above 1, 1 dot above 2, 1 dot above 3, 1 dot above 4, 1 dot above 5, 2 dots above 6.
Option C
D
A dot plot going from 0 to 6. There is 1 dot above 1, 2 dots above 2, 3 dots above 3, 2 dots above 4, 1 dot above 5.
Option D
5

Dylan wanted to find the average number of hours per day that the students in his class practiced their instruments. He chose three students by drawing their names from a hat. What should he do to ensure that he has an accurate average for the class?

Question illustration
A
He should add the three numbers and divide by 3 because that is how one finds an average.
B
He should poll more students to eliminate the variability caused by a sample size that is too small.
C
He should take the middle number as his average since he has three observations.
D
He should just find the average of 0.5 and 4 since 0 does not change anything when adding.
6

Raj polled 100 students in his class to compare the number of hours that teen boys and girls played video games each week. The results of his survey are shown below. Which gender shows greater variability in their playing time?Hours of Video Game Time per Week for Teen Boys Hours of Video Game Time per Week for Teen Girls

Question illustration
A
Boys show greater variability because the 3rd quartile for boys is 17 but only 15 for girls.
B
Boys show greater variability because the median playing time for boys is 14.5 but only 6 for girls.
C
Girls show greater variability because the interquartile range for girls is 12 for girls but only 8 for boys.
D
Girls show greater variability because the data for the girls is skewed toward the lower end of the box plot.
7

Rodell wants to find the favorite gaming app among the students at his school. He decides to poll the thirty students on his football team and the fifteen students on his basketball team to gather the data. What is wrong with Rodell’s method for collecting his data?

A
Rodell only polled fellow athletes; this sample does not represent nonathletes at the school.
B
Rodell needs a larger sample size than two sports teams to represent a whole school.
C
Rodell polled everyone on his teams; he should have only polled every other student for it to be a true sample.
D
Rodell’s polling method only included fall and winter sports; he should have also included a spring sport like baseball.
8

Ariel wants to find out the most popular theme for spirit week at school. She cannot decide between two methods. Option 1: She will poll each student who leaves the gym after sports practice.Option 2: She will randomly poll three students from each first-period class.Which statement about the methods is true?

A
Option 1 is biased.
B
Option 2 is biased.
C
Neither is biased.
D
Both are biased.
9

The dot plot and box plot show different displays of the ages of runners on a track team.Which statements best describe the dot plot or box plot? Check all that apply.

Question illustration
A
Add the number of dots above each age in the dot plot to find the number of players on the team: 2 + 1 + 3 + 2 + 3 + 2 = 13.
B
Subtract the maximum and minimum values of the box plot to find the number of players on the team: 12 – 7.
C
The median appears clearly on the dot plot at the center of the number line: 9.5.
D
The median appears clearly on the box plot at the line within the box: 10.
E
The dot plot is the only display that can be used to show the variability of the data.
F
The box plot is the only display that can be used to show the variability of the data.
10

Madison claims that two data sets with the same median will have the same variability. Which data set would provide good support for whether her claim is true or false?

A
Her claim is true and she should use these data sets to provide support.
Option A
B
Her claim is true and she should use these data sets to provide support.
Option B
C
Her claim is false and she should use these to show that two data sets with the same median can have different variability.
Option C
D
Her claim is false and she should use these to show that two data sets with the same median can have different variability.
Option D
11

Sofia is a helper for the kindergarten class and is in charge of picking a video for their end-of-year party. To choose which type of movie they would like best, she decided to survey every other child entering a matinee for a cartoon called, “Three Pretty Princesses.” The total number of children surveyed was 40. What is wrong with the way she selected her sample? Check all that apply.

A
The sample of 40 children is too small to represent all kindergartners.
B
The sample was taken at a specific movie, which will skew data towards that type of movie.
C
The sample is likely to include a lot more girls than boys, since the movie title is “Three Pretty Princesses.”
D
The sample should include the adults with the children instead of only children.
E
The sample should include the other peer helpers in her grade to include a greater age range.
12

Leo wants to determine the average number of texts middle school students send in a day. Since all middle school students are enrolled in history, he randomly surveyed 4 students from each of Mr. Barnes’s eighth-grade history classes. Ms. Lopez and Mrs. Frank also teach eighth-grade history. What should Leo do to ensure his sample is representative of all middle school students?

A
He should take the sample as is because he randomly surveyed students in each of Mr. Barnes’s classes.
B
He should also take a sample from Ms. Lopez’s and Mrs. Frank’s classes so that each student has the same chance of being chosen.
C
He should also take a sample from each of the other history classes in all of the other grades in the middle school.
D
He should survey all the students in all the history classes to make sure he collects enough data.
13

Phoebe surveyed teens and adults to find the average number of hours of sleep they get during the week. Her results are shown below. Which statement regarding her survey results is true?Hours of Sleep for TeensHours of Sleep for Adults

Question illustration
A
Adults get more hours of sleep on average than teens.
B
Adults have less variability in the hours of sleep.
C
Teens have less variability in the hours of sleep.
D
Teens get less sleep on average than adults.
14

Ethan and three friends kept track of their average points scored in each basketball game over the season. The results are shown below. Which player is the most consistent?Basketball Scoring StatisticsPlayerMean ScoreInterquartile RangeAdam10.91.4Ben16.71.8Ethan14.22.2Joaquin12.90.9

A
Adam, because his mean score is the lowest
B
Ben, because his mean score is the highest
C
Ethan, because his interquartile range is the highest
D
Joaquin, because his interquartile range is the lowest
15

The box plot and histogram show the number of minutes sixth-grade students spent reading the previous night.Which statements best describe the box plot or histogram? Check all that apply.

Question illustration
A
Using the information in the box plot, the total number of students surveyed is 70 – 25, or 45.
B
Using the information in the histogram, the total number of students surveyed is 4 + 4 + 6 + 4 + 2 = 20.
C
Referring to the box plot, the median of the data is 50.
D
Referring to the histogram, the median of the data is 49.5.
E
The range of the data can be found using the box plot.
F
The range of the data can be found using the histogram.
16

How many people were included in the sample shown below?

Question illustration
A
6
B
7
C
17
D
18
17

Mrs. Liang, the librarian, wants to compare the numbers of patrons who prefer e-books to paperback books. She decides to take a poll of every third adult with a child who arrives at the library for one of the four reading groups: toddlers, preschoolers, primary grades, and upper elementary. Which statement is true about her method of data collection?

A
It is balanced because she is including parents with children of all ages so she will get a greater age range.
B
It is not balanced because it is less likely to include teens, young adults, and senior citizens in the patron population.
C
It is not balanced because she only surveyed the adults and not the young children.
D
It is balanced because she is polling four different reading groups, which include all types of people.
18

For a school newspaper article, Cienna conducted a survey to find out students’ favorite subjects. She polled all the students in Mrs. Lopez’s advanced dance class. Why is her data likely to be skewed?

A
Advanced dance students are more likely to enjoy dance than students in the general population, so dance may be overrepresented.
B
Cienna should have interviewed all the students in the school to get more accurate data.
C
Advanced dance students are more likely to enjoy dance than students in the general population, so dance will be underrepresented.
D
Cienna should have interviewed only every other student in the class to avoid having too many people.
19

Jorge wants to find the most popular way for teens to volunteer in the community. He cannot decide between two methods.Option 1: He will ask every fifth person on each English class roster.Option 2: He will attend a walk for charity community event to ask teen participants about the ways they volunteer.Which statement about the methods is true?

A
Option 1 is biased.
B
Option 2 is biased.
C
Neither is biased.
D
Both are biased.

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