The Effect of Extremes

5 min

Narrative

This Warm-up prompts students to think about what variables they may use to analyze a situation. Then, students describe data displays they may use to compare two sets of data. Choosing variables and planning a process for comparing data sets engage students in aspects of mathematical modeling (MP4).

Listen for groups that choose a variable other than the number of wins to determine the top players in the game and for groups that select different data displays or ways of comparing data sets, and ask them to share with the whole group.

Launch

Arrange students in groups of 2.

Ask students, “Have you ever played a game where you did really well, but still lost?” Consider looking up or sharing your own stories of great individual performances that still resulted in a loss. Tell students, “There are often many ways to measure performance and compare results.”

Tell students to think quietly about their answers to the questions for about 1 minute before discussing with their partner and then sharing with the whole group.

Student Task

Several online video games match players with other players at random to compete in a team game.

  1. What information could you use to determine the top players in a team game like this? Explain your reasoning.
  2. There are two games of a similar type. One person claims that the best players play game A. Another person claims that game B has better players. How could you display data to help inform their discussion? Explain your reasoning.

Sample Response

Sample responses:

  1. The number of points obtained by an individual player over several games could help determine the top players. Although wins might also be considered, good players will generally earn more points over several games even if they lose when matched with worse teammates.
  2. I would create dot plots of the number of points gained by the top 100 players in each game. Then I would compare the center and variability of each distribution. 
Activity Synthesis (Teacher Notes)

Select previously identified students to share their solutions. If it does not come up in discussion, ask students how they might interpret a situation in which a small group of players has a significantly greater number of wins or points than the rest of the group. It might mean that most of the players are not very good and there are a few who are, or it might mean that there are a few dominant players who are much better than average players.

Standards
Addressing
  • HSS-ID.A.2·Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
  • S-ID.2·Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
  • S-ID.2·Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
  • S-ID.2·Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
Building Toward
  • HSS-ID.A.3·Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
  • S-ID.3·Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
  • S-ID.3·Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
  • S-ID.3·Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

20 min

10 min