standard_description: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
problem_activity: Warm-up
The mathematical purpose of this activity is for students to compare different distributions using shape, measures of center, and measures of variability. This warm-up prompts students to compare four distributions representing recent bowling scores for potential teammates. It gives students a reason to use language precisely (MP6) and gives you the opportunity to hear how they use terminology and talk about characteristics of the images in comparison to one another.
Launch
Arrange students in groups of 2–4.
Student Facing
Each histogram shows the bowling scores for the last 25 games played by each person. Choose 2 of these people to join your bowling team. Explain your reasoning.
Person A
mean: 118.96
median: 111
standard deviation:​ ​32.96
interquartile range: 44
[IMG]
Person B
mean: 131.08
median: 129
standard deviation: 8.64
interquartile range: 8
[IMG]
Person C
mean: 133.92
median: 145
standard deviation: 45.04
interquartile range: 74
[IMG]
Person D
mean: 116.56
median: 103
standard deviation: 56.22
interquartile range: 31.5
[IMG]
Student Response
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Activity Synthesis
Ask each group to share one bowler they would choose and their reasoning. If none of the groups select a certain player, ask why this player was not chosen or to give reasons why another team may want this player on their team. Since there is no single correct answer to the question of which one does not belong, attend to students’ explanations and ensure the reasons given are correct. During the discussion, ask students to explain how they used the statistics given as well as the histograms.


aligns: no