The population is the whole group you want to know about. A sample is a part of it. A random sample gives everyone the same chance, so it is fair. Asking only friends or only one group is biased.
Worked example
A city wants to know how many residents ride the bus. Which sample is most likely to represent all the residents?
Answer:200 residents chosen by a computer from a list of everyone
The best choice is 200 residents chosen by a computer from a list of everyone. A computer picks from the whole population, so every resident has an equal chance. A sample is fair when it is random, big enough, and drawn from the whole population.
For grown-ups: Random sampling; inference about populations; comparing two populations. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.
CCSS 7.SP.A
What this practises, for teachers
Practices random sampling; inference about populations; comparing two populations (7.SP.A). A printable sheet with its answer key, worked answers on the page, no accounts.
A random sample of 50 students from a school of 500 found that 10 walk to school. About how many of the 500 students walk?
Show the answer and how
Answer:about 100 students
The best choice is about 100 students. 10 of 50 is 1/5, and 1/5 of 500 is 100. A sample is fair when it is random, big enough, and drawn from the whole population.
Which is a random sample of 30 students from a class of 90?
Show the answer and how
Answer:Put every name in a hat and draw 30
The best choice is Put every name in a hat and draw 30. Every student has the same chance of being drawn, so it is random. A sample is fair when it is random, big enough, and drawn from the whole population.
To find the average height of all 7th graders in a district, a researcher measures 80 of them. What is the population?
Show the answer and how
Answer:all 7th graders in the district
The best choice is all 7th graders in the district. The population is the whole group we want to know about: every 7th grader in the district. A sample is fair when it is random, big enough, and drawn from the whole population.
To learn whether people in a city like a new park, a surveyor asks 100 people as they leave the park. Why might this sample be a poor one?
A principal wants to know the favorite lunch of all 600 students. Which sample is most likely to represent the whole school?
To learn whether people in a city like a new park, a surveyor asks 100 people as they leave the park. Why might this sample be a poor one?
Which is a random sample of 30 students from a class of 90?
To find the average height of all 7th graders in a district, a researcher measures 80 of them. What is the population?
To find the average height of all 7th graders in a district, a researcher measures 80 of them. What is the population?
To learn whether people in a city like a new park, a surveyor asks 100 people as they leave the park. Why might this sample be a poor one?
Which is a random sample of 30 students from a class of 90?
To find the average height of all 7th graders in a district, a researcher measures 80 of them. What is the population?
Two random samples are taken from the same town to estimate how many people own a bike. One has 20 people and one has 400. Which gives the better estimate?
Which is a random sample of 30 students from a class of 90?
A teacher wants to estimate how many of 1,000 students own a pet. Which sample is best?
Answer key
Only people who already visit the park were asked, so they may like it more than others do
40 students chosen at random from the school's list
Only people who already visit the park were asked, so they may like it more than others do
Put every name in a hat and draw 30
all 7th graders in the district
all 7th graders in the district
Only people who already visit the park were asked, so they may like it more than others do