Definitions
Define "population"
The entire group you want information about.
A student wants to know the most popular type of skateboard used at Central Skate Park. She surveys skaters who are at the park on Saturday morning.
Which TWO statements about this survey are true?
A. The sample is representative of all skaters
B. The population is all skaters at Central Skate Park
C. The sample includes every skater
D. The results may be biased by time or day
B. The population is all skaters at Central Skate Park
D. The results may be biased by time or day
A representative sample of students at Oakwood Middle School was surveyed about their favorite type of pet.
In the sample:
12 students prefer dogs
8 students prefer cats
4 students prefer other pets
There are 240 students at the school.
Estimate how many students prefer cats.
80 students
A representative sample of students was surveyed about their favorite ice cream flavor.
In the sample:
20 students prefer chocolate
12 students prefer vanilla
8 students prefer strawberry
Which inferences are valid? Select all that apply.
A. Students are more likely to prefer chocolate than any other flavor.
B. More students prefer chocolate than strawberry.
C. Most students at the school prefer vanilla.
D. All students at the school like ice cream.
A. Students are more likely to prefer chocolate than any other flavor.
B. More students prefer chocolate than strawberry.
A representative sample of students at Lincoln Middle School was surveyed about whether they use a locker.
Can the results be used to make a valid inference about all students at Lincoln Middle School?
Yes, the sample represents the school population.
Define "sample"
A smaller group taken from the population to represent it.
A student council wants to know the most popular lunch choice at Jefferson Middle School. They randomly survey 100 students from all grade levels.
Which TWO statements are true?
A. The population is all students at Jefferson Middle School.
B. The sample is representative of the population.
C. The survey is biased because only some students were surveyed.
D. The sample only includes students who eat lunch at the same time.
A. The population is all students at Jefferson Middle School.
B. The sample is representative of the population.
A representative sample of students was surveyed about how they get to school.
In the sample:
15 students ride the bus
10 students walk
5 students are driven
There are 300 students in the school.
Estimate how many students walk to school.
100 students
A representative sample of students was surveyed about how they get to school.
In the sample:
15 students ride the bus
10 students walk
5 students are driven
Which inferences are valid? Select all that apply.
A. Students are more likely to ride the bus than walk.
B. Fewer students are driven to school than use other methods.
C. Most students in the school walk to school.
D. All students use the same method to get to school.
A. Students are more likely to ride the bus than walk.
B. Fewer students are driven to school than use other methods.
A teacher surveys a representative sample of students in her class about whether they like listening to music while working.
Can she use the results to make a valid inference about all students in the school?
No, one class does not represent the entire school population.
Define "median"
The middle value in a set of numbers when they are ordered from least to greatest.
A teacher wants to know the most popular after-school club at Lincoln Middle School. She surveys students who stay late on Tuesdays.
Which TWO statements are true?
A. The population is all students at Lincoln Middle School.
B. The sample is representative of all students at the school.
C. The survey may be biased because not all students stay late.
D. The survey includes a random sample of students.
A. The population is all students at Lincoln Middle School.
C. The survey may be biased because not all students stay late.
A representative sample of students was surveyed about how many hours they spend streaming videos each week.
In the sample:
14 students stream less than 5 hours
21 students stream 5–10 hours
15 students stream more than 10 hours
There are 420 students at the school.
Estimate how many students stream 5–10 hours per week.
176 students
A representative sample of students was surveyed about how long they spend on homework each night.
In the sample:
14 students spend less than 30 minutes
18 students spend 30–60 minutes
8 students spend more than 60 minutes
Which inferences are valid? Select all that apply.
A. Students are more likely to spend 30–60 minutes on homework than any other amount of time.
B. More students spend less than 30 minutes than more than 60 minutes.
C. Most students spend more than an hour on homework each night.
D. Every student spends some time on homework.
A. Students are more likely to spend 30–60 minutes on homework than any other amount of time.
B. More students spend less than 30 minutes than more than 60 minutes.
A representative sample of students at a middle school was surveyed about how often they visit the library.
Can the results be used to make a valid inference about middle school students in the district?
No, students from one school do not represent all schools in the district.
Define "representative sample"
A sample that accurately reflects the population.
A teacher wants to know whether students like having a monthly school spirit day. She randomly selects 50 students from a list of all students in the school and surveys them.
Which TWO statements are true?
A. The population is all students at the school.
B. The sample is representative because it was randomly selected.
C. The survey is biased because the sample size is small.
D. The sample only includes students who like school events.
A. The population is all students at the school.
B. The sample is representative because it was randomly selected.
A representative sample of students was surveyed about how many cell phones they own.
In the sample:
18 students own no phone
27 students own 1 phone
15 students own 2 or more phones
There are 360 students at the school.
Estimate how many students own exactly one phone.
162 students
A representative sample of students was surveyed about how they usually listen to music.
In the sample:
22 students use headphones
16 students use speakers
12 students do not listen to music
Which inferences are valid? Select all that apply.
A. Students are more likely to use headphones than speakers.
B. More students listen to music than do not listen to music.
C. Most students never listen to music.
D. All students prefer listening to music with headphones.
A. Students are more likely to use headphones than speakers.
B. More students listen to music than do not listen to music.
A representative sample of adults who attend a local gym was surveyed about how often they exercise.
Can the results be used to make a valid inference about all adults in the town?
No, people who go to a gym are not representative of all adults.
Define "valid inference"
A conclusion about a population that is supported by data from a representative sample.
A principal wants to know the most common way students get to school. She surveys students who arrive early for morning tutoring.
Which TWO statements are true?
A. The population is all students at the school.
B. The sample is representative of the population.
C. The results may be biased because not all students attend tutoring.
D. The survey includes a random sample of students.
A. The population is all students at the school.
C. The results may be biased because not all students attend tutoring.
A representative sample of students was surveyed about their main weekend activity.
In the sample:
16 students play sports
14 students spend time with friends
10 students stay home
There are 280 students at the school.
Estimate how many students spend time with friends on weekends.
98 students
A representative sample of students was surveyed about the number of Internet-compatible devices they own.
In the sample:
18 students own 1 device
25 students own 2 devices
7 students own 3 or more devices
Which inferences are valid? Select all that apply.
A. Students are more likely to own exactly 2 devices than any other number.
B. More students own exactly 2 devices than own 3 or more devices.
C. Most students at the school own 3 or more devices.
D. Every student at the school owns at least one device.
A. Students are more likely to own exactly 2 devices than any other number.
B. More students own exactly 2 devices than own 3 or more devices.
A representative sample of residents from all neighborhoods in a town was surveyed about Internet access at home.
Can the results be used to make a valid inference about the town’s residents?
Yes, the sample represents the entire population being studied.