Populations, samples, parameters and statistics

About this lesson

Algebra II › Statistical inference

To save a PDF, choose “Save as PDF” in the print dialog.

Populations, samples, parameters and statistics

Warm-up

Three quick questions from earlier lessons.

Discover

A poll of 1,000 voters finds 52% support for a candidate. Is 52% the support among all voters?

  1. Not exactly: it estimates it
  2. Yes

Key idea

We study a sample to learn about a population.

The population is the whole group of interest; a sample is the part we actually observe. A parameter is a number describing the population (usually unknown); a statistic is a number computed from the sample, used to estimate the parameter.

Worked example

A factory tests 200 of today's 10,000 bulbs; 3% are faulty.

Population: the 10,000 bulbs
Everything produced today.
Sample: the 200 bulbs
Those tested.
3% is a statistic estimating the faulty rate today
Computed from the sample.

Your turn, guided

Your turn: how many faulty bulbs were found in the sample?

66
3% of 200.

Practice ★

  1. A researcher measures the sleep of 376 randomly chosen teenagers and finds a mean of 7.1 hours. What is 7.1?
    1. A statistic: it describes the sample
    2. A parameter: it describes all teenagers
    3. The population
  1. To learn how much US college students spend on books, a team surveys 671 students at 20 colleges. What is the population?
    1. All US college students
    2. The 671 students surveyed
    3. The 20 colleges

Watch out!

Practice ★★

  1. Census records show that 52% of all households in a town own a car. What is 52%?
    1. A parameter: it describes the whole population
    2. A statistic
    3. A sample proportion

Exit ticket

Three questions to check you have got it.

  1. A researcher measures the sleep of 376 randomly chosen teenagers and finds a mean of 7.1 hours. What is 7.1?
    1. A statistic: it describes the sample
    2. A parameter: it describes all teenagers
    3. The population
  2. A researcher measures the sleep of 288 randomly chosen teenagers and finds a mean of 7.1 hours. What is 7.1?
    1. A statistic: it describes the sample
    2. A parameter: it describes all teenagers
    3. The population
  3. A researcher measures the sleep of 121 randomly chosen teenagers and finds a mean of 7.1 hours. What is 7.1?
    1. A statistic: it describes the sample
    2. A parameter: it describes all teenagers
    3. The population

Summary card

Population and sample

  • Population → parameter (usually unknown).
  • Sample → statistic (an estimate).

Watch out: a number from the sample is a statistic.

End of the lesson

Next lesson: Bias in sampling Back to the chapter

Answers: Populations, samples, parameters and statistics

A

  1. A statistic: it describes the sample

B

  1. All US college students

C

  1. A parameter: it describes the whole population

D

  1. A statistic: it describes the sample
  2. A statistic: it describes the sample
  3. A statistic: it describes the sample

CC BY-SA 4.0