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Math Coach Amy
Amy Ferguson Moncure

7th Grade Math ยท Unit 1

Representative
Samples

Decide whether a sample is random and whether it can represent the group.

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Key Ideas Easy Medium Hard
What to Remember

Equal chance

A random sample gives every member of the group you care about an equal chance to be chosen.

Name that group first. A random sample of one class is not a random sample of the whole school.

Not random

The first people in line are a convenience sample. Whoever answers a post is a voluntary sample.

Only your friends, or only one class when you mean the whole school, is one subgroup. Those are not random samples of the larger group.

Size does not fix bias

A very small sample, such as 5 students for a whole school, can be too small to represent the whole school even when the draw is random. There is no magic sample size.

A large biased sample is still biased. A larger random sample usually represents the group better. A bigger sample is not better if it was chosen badly.

Level 1

Easy

Say yes or no, and say why.

Example
Is this selection random? The first 20 students in the lunch line are asked about the whole school.

A random sample gives every member of the group an equal chance to be chosen.

This is convenience. Students are chosen because they are first in line, so the other students had no equal chance.

This selection is not random.

Answer: No. This is convenience. Students are chosen because they are first in line, so the other students had no equal chance.

1
Is this selection random? Every seventh grader's name is on a card. The cards are mixed, and 30 cards are drawn to describe the seventh grade.
Show Answer

A random sample gives every member of the group an equal chance to be chosen.

Every seventh grader has an equal chance to be drawn.

This selection is random.

Answer: Yes. Every seventh grader has an equal chance to be drawn.

2
Is this selection random? A post says to reply if you want to tell your bus time. Whoever replies is the sample for the whole school.
Show Answer

A random sample gives every member of the group an equal chance to be chosen.

This is voluntary. Only people who choose to answer the post are included.

This selection is not random.

Answer: No. This is voluntary. Only people who choose to answer the post are included.

3
Is this selection random? You ask only your friends about the pets of every family on the street.
Show Answer

A random sample gives every member of the group an equal chance to be chosen.

Friends are one subgroup. The other families had no chance.

This selection is not random.

Answer: No. Friends are one subgroup. The other families had no chance.

4
Is this selection random? Every player on the soccer team has a number, and 8 numbers are drawn to describe that team.
Show Answer

A random sample gives every member of the group an equal chance to be chosen.

Every player on the team has an equal chance. The group is the team.

This selection is random.

Answer: Yes. Every player on the team has an equal chance. The group is the team.

5
Is this selection random? One class is asked about the lunch choices of the whole school.
Show Answer

A random sample gives every member of the group an equal chance to be chosen.

One class is a subgroup. Students in the other classes had no chance.

This selection is not random.

Answer: No. One class is a subgroup. Students in the other classes had no chance.

6
Is this selection random? A random number list picks students so that each student in the school has an equal chance.
Show Answer

A random sample gives every member of the group an equal chance to be chosen.

Each student in the school has an equal chance.

This selection is random.

Answer: Yes. Each student in the school has an equal chance.

7
Is this selection random? You ask the students sitting nearest the door about the whole class.
Show Answer

A random sample gives every member of the group an equal chance to be chosen.

This is convenience. Students farther from the door had no equal chance.

This selection is not random.

Answer: No. This is convenience. Students farther from the door had no equal chance.

8
Is this selection random? Every dog at the park gets a number, and 10 numbers are drawn to describe the dogs at the park.
Show Answer

A random sample gives every member of the group an equal chance to be chosen.

Every dog at the park has an equal chance.

This selection is random.

Answer: Yes. Every dog at the park has an equal chance.

9
Is this selection random? Only the athletes are asked about the bus rides of the whole school.
Show Answer

A random sample gives every member of the group an equal chance to be chosen.

Athletes are one subgroup. The other students had no chance.

This selection is not random.

Answer: No. Athletes are one subgroup. The other students had no chance.

10
Is this selection random? Every song on the class playlist is written on a card, and 12 cards are drawn.
Show Answer

A random sample gives every member of the group an equal chance to be chosen.

Every song on that playlist has an equal chance.

This selection is random.

Answer: Yes. Every song on that playlist has an equal chance.

Level 2

Medium

Give a verdict: random or not, and whether the size can represent that group.

Example
Is the sample random, and is it large enough for the group named here? You draw 40 names so that each of 200 seventh graders has an equal chance. You want to describe the seventh grade.

Check the group you care about. Every member of that group needs an equal chance.

A large biased sample is still biased. A tiny random sample can be too small to represent the group.

Every seventh grader had an equal chance, and the sample is not a handful.

Answer: Yes. It is random, and 40 students is not a tiny sample of 200, so it can represent the seventh grade.

1
Is the sample random, and is it large enough for the group named here? 180 students reply to a post about lunch. The school has 500 students, and you want the whole school.
Show Answer

Check the group you care about. Every member of that group needs an equal chance.

A large biased sample is still biased. A tiny random sample can be too small to represent the group.

Whoever answers a post is not every student. A large biased sample is still biased.

Answer: No. It is not random. The replies are voluntary. It is large, but size does not fix the bias.

2
Is the sample random, and is it large enough for the group named here? The first 120 students in the lunch line are asked about a school of 400.
Show Answer

Check the group you care about. Every member of that group needs an equal chance.

A large biased sample is still biased. A tiny random sample can be too small to represent the group.

Convenience does not become fair when the line is long.

Answer: No. It is not random. They are the first people in line. It is large, but size does not fix the bias.

3
Is the sample random, and is it large enough for the group named here? 5 names are drawn so that each of the 700 students has an equal chance. You want the whole school.
Show Answer

Check the group you care about. Every member of that group needs an equal chance.

A large biased sample is still biased. A tiny random sample can be too small to represent the group.

The draw is fair, and 5 students are still too small to represent the whole school.

Answer: It is random, but it is too small to represent the whole school.

4
Is the sample random, and is it large enough for the group named here? 4 dogs are drawn so that each of the 90 dogs at the park event has an equal chance.
Show Answer

Check the group you care about. Every member of that group needs an equal chance.

A large biased sample is still biased. A tiny random sample can be too small to represent the group.

Every dog had an equal chance, and 4 dogs are too small to represent all the dogs at the park.

Answer: It is random, but it is too small to represent all the dogs at the park.

5
Is the sample random, and is it large enough for the group named here? 25 songs are drawn so that each of 120 songs on the school playlist has an equal chance.
Show Answer

Check the group you care about. Every member of that group needs an equal chance.

A large biased sample is still biased. A tiny random sample can be too small to represent the group.

Every song had an equal chance. This is not a handful of the playlist.

Answer: Yes. It is random, and 25 songs is not a tiny sample of 120, so it can represent that playlist.

6
Is the sample random, and is it large enough for the group named here? All 27 students in one class are asked about a school of 650.
Show Answer

Check the group you care about. Every member of that group needs an equal chance.

A large biased sample is still biased. A tiny random sample can be too small to represent the group.

Students outside that class had no chance, so the class does not represent the school.

Answer: No. It is not a random sample of the whole school. One class is a subgroup.

7
Is the sample random, and is it large enough for the group named here? 15 friends are asked about the bus rides of all 300 bus riders.
Show Answer

Check the group you care about. Every member of that group needs an equal chance.

A large biased sample is still biased. A tiny random sample can be too small to represent the group.

The other riders had no chance.

Answer: No. It is not random. Friends are one subgroup of the riders.

8
Is the sample random, and is it large enough for the group named here? All 160 athletes are asked about lunch for a school of 600.
Show Answer

Check the group you care about. Every member of that group needs an equal chance.

A large biased sample is still biased. A tiny random sample can be too small to represent the group.

A large biased sample is still biased.

Answer: No. It is not random. Athletes are one subgroup. The sample is large, but size does not fix the bias.

9
Is the sample random, and is it large enough for the group named here? You number every bus rider and draw 30 names so each of the 240 riders has an equal chance.
Show Answer

Check the group you care about. Every member of that group needs an equal chance.

A large biased sample is still biased. A tiny random sample can be too small to represent the group.

Every rider had an equal chance. The sample is not a handful.

Answer: Yes. It is random, and 30 riders is not a tiny sample of 240, so it can represent the riders.

10
Is the sample random, and is it large enough for the group named here? A garden club post gets 90 replies about tomato height, but you want the heights of the 30 plants in your own garden.
Show Answer

Check the group you care about. Every member of that group needs an equal chance.

A large biased sample is still biased. A tiny random sample can be too small to represent the group.

A large sample of a different group does not represent your garden.

Answer: No. The replies are not your plants. The sample is large, but size does not fix the bias.

Level 3

Hard

Name the group, the random draw, and whether you need a larger sample.

Example
This plan is weak. Tell how to make a random sample of the group you actually care about, and say whether the sample needs to be larger. You will ask the first 100 students in the lunch line about a school of 500.

Group: every student in the school

Random draw: Put every student name in a drawing so each student has an equal chance.

Larger: No. 100 is not the problem. These are the first people in line, and size does not fix the bias.

Answer: Group: every student in the school
Random draw: Put every student name in a drawing so each student has an equal chance.
Larger: No. 100 is not the problem. These are the first people in line, and size does not fix the bias.

1
This plan is weak. Tell how to make a random sample of the group you actually care about, and say whether the sample needs to be larger. 250 people answer a post, and you want to describe a school of 500.
Show Answer

Group: every student in the school

Random draw: Draw names from the school list so each student has an equal chance. Do not collect more post replies.

Larger: No. A large voluntary sample is still biased, and size does not fix the bias. A smaller random sample can represent the school better.

Answer: Group: every student in the school
Random draw: Draw names from the school list so each student has an equal chance. Do not collect more post replies.
Larger: No. A large voluntary sample is still biased, and size does not fix the bias. A smaller random sample can represent the school better.

2
This plan is weak. Tell how to make a random sample of the group you actually care about, and say whether the sample needs to be larger. You draw 5 names at random from 800 students to describe bus rides for the whole school.
Show Answer

Group: every student in the school

Random draw: Keep a draw in which each student has an equal chance.

Larger: Yes. Five students are too small to represent the whole school.

Answer: Group: every student in the school
Random draw: Keep a draw in which each student has an equal chance.
Larger: Yes. Five students are too small to represent the whole school.

3
This plan is weak. Tell how to make a random sample of the group you actually care about, and say whether the sample needs to be larger. You ask your 6 friends about pets for 200 families in the neighborhood.
Show Answer

Group: the 200 families

Random draw: List the families and draw so each family has an equal chance.

Larger: Yes. Six friends are one subgroup, and they are too small to represent 200 families.

Answer: Group: the 200 families
Random draw: List the families and draw so each family has an equal chance.
Larger: Yes. Six friends are one subgroup, and they are too small to represent 200 families.

4
This plan is weak. Tell how to make a random sample of the group you actually care about, and say whether the sample needs to be larger. You survey one class of 32 students and use them for a school of 900.
Show Answer

Group: every student in the school

Random draw: Draw from the whole school so each student has an equal chance.

Larger: No. It does not need to be larger than a fair sample. One class is the wrong subgroup, and size does not fix the bias.

Answer: Group: every student in the school
Random draw: Draw from the whole school so each student has an equal chance.
Larger: No. It does not need to be larger than a fair sample. One class is the wrong subgroup, and size does not fix the bias.

5
This plan is weak. Tell how to make a random sample of the group you actually care about, and say whether the sample needs to be larger. You measure the first 8 tomato plants in the first row. The garden has 150 plants.
Show Answer

Group: all 150 plants in the garden

Random draw: Number every plant and draw so each plant has an equal chance.

Larger: Yes. Eight plants from the first row are a convenience sample, and 8 is too small to represent the whole garden.

Answer: Group: all 150 plants in the garden
Random draw: Number every plant and draw so each plant has an equal chance.
Larger: Yes. Eight plants from the first row are a convenience sample, and 8 is too small to represent the whole garden.

6
This plan is weak. Tell how to make a random sample of the group you actually care about, and say whether the sample needs to be larger. You ask all 200 band members about lunch for a school of 700.
Show Answer

Group: every student in the school

Random draw: Draw from the whole school, not only from the band.

Larger: No. It does not need to be larger. Band members are one subgroup, and size does not fix the bias.

Answer: Group: every student in the school
Random draw: Draw from the whole school, not only from the band.
Larger: No. It does not need to be larger. Band members are one subgroup, and size does not fix the bias.

7
This plan is weak. Tell how to make a random sample of the group you actually care about, and say whether the sample needs to be larger. Every bus rider's name is in a hat. You draw 5 names to describe all 400 riders.
Show Answer

Group: all 400 bus riders

Random draw: Keep drawing so every rider has an equal chance.

Larger: Yes. Five riders are too small to represent all the bus riders.

Answer: Group: all 400 bus riders
Random draw: Keep drawing so every rider has an equal chance.
Larger: Yes. Five riders are too small to represent all the bus riders.

8
This plan is weak. Tell how to make a random sample of the group you actually care about, and say whether the sample needs to be larger. You use the 40 people who happen to be in the garden after school to describe bus rides for 600 students.
Show Answer

Group: every student in the school

Random draw: Draw from the school list. Do not use only the people who are already in the garden.

Larger: No. Forty is not a tiny number, but this is convenience, and size does not fix the bias.

Answer: Group: every student in the school
Random draw: Draw from the school list. Do not use only the people who are already in the garden.
Larger: No. Forty is not a tiny number, but this is convenience, and size does not fix the bias.

9
This plan is weak. Tell how to make a random sample of the group you actually care about, and say whether the sample needs to be larger. 300 strangers answer a post about song length. The group you care about is the 80 songs on the class playlist.
Show Answer

Group: the 80 songs on the class playlist

Random draw: Write each song on a card, draw so each song has an equal chance, and record the length of each drawn song.

Larger: No. You do not need 300 replies. The post is the wrong group, and size does not fix the bias.

Answer: Group: the 80 songs on the class playlist
Random draw: Write each song on a card, draw so each song has an equal chance, and record the length of each drawn song.
Larger: No. You do not need 300 replies. The post is the wrong group, and size does not fix the bias.

10
This plan is weak. Tell how to make a random sample of the group you actually care about, and say whether the sample needs to be larger. You draw 5 songs at random from a school playlist of 200 songs to describe the lengths.
Show Answer

Group: every song on the school playlist

Random draw: Keep a draw so each song has an equal chance, then record the length of each drawn song.

Larger: Yes. Five songs are too small to represent the whole playlist.

Answer: Group: every song on the school playlist
Random draw: Keep a draw so each song has an equal chance, then record the length of each drawn song.
Larger: Yes. Five songs are too small to represent the whole playlist.

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