Practice Population vs Sample in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A population is the entire group you want to study. A sample is a smaller subset of that population that you actually collect data from.

You cannot taste every cookie in the bakery to check quality โ€” you taste a few (sample) and draw conclusions about the whole batch (population).

Showing a random 20 of 50 problems.

Example 1

easy
A scientist wants to know the average weight of all redwood trees in California. She measures 80 trees. What is the population?

Example 2

easy
A researcher studies all 500 students in a school by surveying 50 of them. What are the 50?

Example 3

medium
Why does a larger random sample usually give a better estimate?

Example 4

medium
A magazine surveys readers via mail; 8% respond. Why is the resulting sample likely biased?

Example 5

easy
True or false: the sample is always smaller than the population.

Example 6

hard
A random sample gives xห‰=84\bar{x}=84. A second random sample from the same population gives xห‰=86\bar{x}=86. Why aren't they equal?

Example 7

medium
A city has 40% homeowners. A truly representative sample of 250 residents should contain about how many homeowners?

Example 8

medium
A census measures EVERY person in a country. Is that a sample or the population?

Example 9

easy
You ask 30 customers at a coffee shop their favorite drink. What is the sample size?

Example 10

medium
A college has 12,000 students. A survey of 400 finds 62% own a car. Which number is the parameter and which is the statistic?

Example 11

medium
A magazine's online poll gets 8,000 responses. What kind of sample is this likely to be?

Example 12

medium
Which is better: a random sample of 100 or a biased sample of 1000?

Example 13

easy
You read every page of a 300-page book to count words on each. Sample or population?

Example 14

medium
A national poll calls 1,000 random adults. What is the population, and what is the sample size?

Example 15

medium
A sample mean is xห‰=12.4\bar{x}=12.4 and the population mean is ฮผ=12.0\mu=12.0. The difference xห‰โˆ’ฮผ=0.4\bar{x}-\mu=0.4 is called what?

Example 16

hard
You want the population mean weekly screen time of US teens. You only have data on 12 of your cousins. List two reasons this sample is poor.

Example 17

medium
In a sample of 50, the mean test score is 78. Does this prove the population mean is 78?

Example 18

challenge
You want to generalize to ALL teens but sample only a coding-camp. What's the threat to validity?

Example 19

easy
Which symbol denotes a sample mean?

Example 20

easy
A value describing the whole population (like the true mean) is called a what?