Introduction to Sampling (College Board AP® Statistics)

Introduction to sampling

What are populations and samples?

• A population is the set of all the possible elements (items / subjects / individuals) that you could study

• A sample is a smaller subset of the population that you choose to study

  • This means the sample size, , is smaller than the population size,

• You can use a sample to try to learn about the population

  • This is called generalizing

What is a sampling frame?

• A sampling frame is a list (or database) of all the elements in the population

  • e.g. a register of the names of all the students at a high school, in alphabetical order by surname

• From this list, you can select your sample

What does sampling with or without replacement mean?

• When selecting elements from the population to use in a sample

  • sampling with replacement means elements can be selected more than once

  • sampling without replacement means elements can only be selected once

What does it mean for a sample to be representative?

• A sample is representative of its population if the elements in it reflect similar patterns and behaviors to the population

  • One way to make a sample representative is to randomly select its elements from the population

What is variability due to sampling?

• A sample is unlikely to be exactly representative of its population

  • e.g. 3 out of 10 children sampled in a school were found to be left-handed, even though only 20% of children in the school are left-handed

• This natural difference that happens in reality is known as variability due to sampling

What is a census?

• A census is when you study the entire population

When can I use samples to make conclusions about populations?

• You can only generalize conclusions from samples to their populations if the sample has been randomly selected

  • or the sample is representative in some other way