Lesson 19: Comparing Populations With Friends

Let's ask important questions to compare groups.

19.1: Features of Graphic Representations

Dot plots, histograms, and box plots are different ways to represent a data set graphically.

Which of those displays would be the easiest to use to find each feature of the data?

  1. the mean
  2. the median
  3. the mean absolute deviation
  4. the interquartile range
  5. the symmetry
 

19.2: Info Gap: Comparing Populations

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

If your teacher gives you the problem card:

  1. Silently read your card, and think about what information you need to answer the question.
  2. Ask your partner for the specific information that you need.
  3. Explain to your partner how you are using the information to solve the problem.
  4. Solve the problem, and explain your reasoning to your partner.

If your teacher gives you the data card:

  1. Silently read the information on your card.
  2. Ask your partner, “What specific information do you need?” Wait for your partner to ask for information. Only give information that is on your card. (Do not figure out anything for your partner!)
  3. Before telling your partner the information, ask “Why do you need that information?”
  4. After your partner solves the problem, ask them to explain their reasoning, and listen to their explanation.

Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.

19.3: Comparing to Known Characteristics

  1. A college graduate is considering two different companies to apply to for a job. Acme Corp lists this sample of salaries on their website:
    \$45,000 \$55,000 \$140,000 \$70,000 \$60,000 \$50,000

    What typical salary would Summit Systems need to have to be meaningfully different from Acme Corp? Explain your reasoning.

  2. A factory manager is wondering whether they should upgrade their equipment. The manager keeps track of how many faulty products are created each day for a week.
    6 7 8 6 7 5 7
    The new equipment guarantees an average of 4 or fewer faulty products per day. Is there a meaningful difference between the new and old equipment? Explain your reasoning.

Summary

When using samples to comparing two populations, there are a lot of factors to consider.

  • Are the samples representative of their populations? If the sample is biased, then it may not have the same center and variability as the population.
  • Which characteristic of the populations makes sense to compare—the mean, the median, or a proportion?
  • How variable is the data? If the data is very spread out, it can be more difficult to make conclusions with certainty.

Knowing the correct questions to ask when trying to compare groups is important to correctly interpret the results.

Practice Problems ▶