What Makes a Good Sample?

Warmup

Activity #1

Identify Population Samples.

• Move the slider to select the problem number. ​
• Attempt the question before clicking on the check boxes to see the correct answers.

Activity #2

Calculate Measures of Central Tendency.

A young artist sold her first two paintings for \$50 and \$350 out of 10 paintings sold.

(1.) Calculate the mean.

At a gallery show, she sold three paintings for \$250, \$400, and \$1,200.

(2.) Calculate the mean and median.

Her oil paintings were sold for \$410, \$400, and \$375.

(3.) Calculate the mean and median.

Here are the selling prices for all 10 of her paintings:

Activity #3

Practice Exercise Questions.

The price per pound of catfish at a fish market was recorded for 100 weeks.

Here are dot plots showing the population and three different samples from that population.

(1.) What do you notice?

(2.) If the goal is to have the sample represent the population, which of the samples would work best?

(3.) Which wouldn’t work so well? Explain your reasoning.

Challenge #1

How many different outcomes are in each sample space? Explain your reasoning. (You do not need to write out the actual options, just provide the number and your reasoning.)

(1.) A letter of the English alphabet is followed by a digit from 0 to 9.

(2.) A baseball team’s cap is selected from 3 different colors, 2 different clasps, and 4 different locations for the team logo. A decision is made to include or not to include reflective piping.

(3.) A locker combination like 7-23-11 uses three numbers, each from 1 to 40. Numbers can be used more than once, like 7-23-7.

Challenge #2

Here below is a dot plot of the scores on a video game for a population of 50 teenagers.

The three dot plots below are the scores of teenagers in three samples from this population.

Which of the three samples is most representative of the population? Explain how you know.

Challenge #3

When doing a statistical study, it is important to keep the goal of the study in mind. Representative samples give us the best information about the distribution of the population as a whole, but sometimes a representative sample won’t work for the goal of a study!

For example, suppose you want to study how discrimination affects people in your town. Surveying a representative sample of people in your town would give information about how the population generally feels, but might miss some smaller groups. Describe a way you might choose a sample of people to address this question.