Random sampling worksheet

Grade 7 math, Common Core 7.SP.A.1. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Random sampling

Grade 7 math, Common Core 7.SP.A.1

Answer each question about samples.

1.
To find the most popular music, a radio station asks people who call in to the show. Is this a fair sample?
2.
To find out how students get to school, a teacher picks 40 names at random from a list of every student. Is this a fair sample?
3.
To learn how much students read, the librarian surveys only students visiting the library. Is this a fair sample?
4.
In a random sample of 25 students, 18 prefer pizza for lunch. About how many of the 325 students at the school prefer pizza for lunch?
5.
In a random sample of 25 students, 23 prefer pizza for lunch. About how many of the 625 students at the school prefer pizza for lunch?
6.
In a random sample of 25 students, 18 walk to school. About how many of the 500 students at the school walk to school?
7.
In a random sample of 20 students, 8 walk to school. About how many of the 580 students at the school walk to school?
8.
In a random sample of 40 students, 16 play an instrument. About how many of the 960 students at the school play an instrument?
9.
In a random sample of 40 students, 16 walk to school. About how many of the 1,080 students at the school walk to school?
10.
In a random sample of 50 students, 23 have a pet. About how many of the 1,150 students at the school have a pet?

Answer key: Random sampling

Grade 7 math. Each answer has a few worked steps, to help check the method as well as the answer.

1. No. Only people listening to that station can call in.
2. Yes. Every student had the same chance of being chosen.
3. No. Library visitors probably read more than most students.
4. About 234 students
1825 × 325 = 234
5. About 575 students
2325 × 625 = 575
6. About 360 students
1825 × 500 = 360
7. About 232 students
25 × 580 = 232
8. About 384 students
25 × 960 = 384
9. About 432 students
25 × 1,080 = 432
10. About 529 students
2350 × 1,150 = 529

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About random sampling

A sample is a smaller group chosen to learn about a whole population. A random sample gives everyone the same chance of being picked, so it tends to represent the population fairly. A biased sample, like asking only the soccer team about favorite sports, can give misleading results. Results from a fair sample can predict results for the whole population.

Worked example 1

In a random sample of 40 students, 15 walk to school. About how many of the 640 students at the school walk to school?

Step 1.38 × 640 = 240

Answer: About 240 students

Example 2

To find the favorite sport at school, Ava asks 30 players on the soccer team. Is this a fair sample?

Answer: No. Soccer players are likely to choose soccer, so they don’t represent all students.

Watch out for

Ask: does everyone in the population have the same chance of being chosen?
Who is asked matters as much as how many.
To predict, use the same fraction as the sample: 18 out of 50 is 36%.

Practice random sampling online

On StudyWiz, your kid can practice random sampling with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

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