Comparing Data Sets
10 min
Narrative
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. Tell students that bowling is a game in which a higher score is better and the maximum score is 300. It is typical for non-professional bowlers to score a little over 100.
Student Task
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
Person B
- mean: 131.08
- median: 129
- standard deviation: 8.64
- interquartile range: 8
Person C
- mean: 133.92
- median: 145
- standard deviation: 45.04
- interquartile range: 74
Person D
- mean: 116.56
- median: 103
- standard deviation: 56.22
- interquartile range: 31.5
Sample Response
Reasons for each bowler:
- Although Person A has a low mean score, the large variability of scores indicates that this person can score well sometimes. This person’s scores are spread out, and it is not rare for this person to score over 140.
- Person B is very consistent. Although this person does not have great games like the other players, Person B’s mean score is near the top, and this person will reliably get a score between 120 and 160.
- Person C has a high mean score but has scores that are also really variable. This person had the lowest score in this group but has the greatest median score. I think we could coach this person to be more consistent, so this wild card could be on my team.
- Person D has the lowest mean, but is also capable of bowling a near perfect game (twice). This person had two games with scores that were much greater than anyone else’s on the list, so maybe Person D does well when it counts.
Activity Synthesis (Teacher Notes)
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 give reasons why another team may want this player on their team. If time allows, ask if there is any additional information that might make that player more desirable. For example, knowing the conditions behind each score might be helpful. Player C might be a new bowler, and the lower scores might have been when Player C was learning, but the newer scores may all be closer to 200. Player D might not take practice seriously, but can bowl a perfect game in competition.
Because there is no single correct answer, attend to students’ explanations, and ensure that the reasons given are correct. During the discussion, ask students to explain how they used the statistics given as well as the histograms.
Standards
- HSS-ID.A.1·Represent data with plots on the real number line (dot plots, histograms, and box plots).
- S-ID.1·Represent data with plots on the real number line (dot plots, histograms, and box plots).
- S-ID.1·Represent data with plots on the real number line (dot plots, histograms, and box plots).
- S-ID.1·Represent data with plots on the real number line (dot plots, histograms, and box plots).
- 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.
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Comparing Data Sets
10 min
Narrative
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. Tell students that bowling is a game in which a higher score is better and the maximum score is 300. It is typical for non-professional bowlers to score a little over 100.
Student Task
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
Person B
- mean: 131.08
- median: 129
- standard deviation: 8.64
- interquartile range: 8
Person C
- mean: 133.92
- median: 145
- standard deviation: 45.04
- interquartile range: 74
Person D
- mean: 116.56
- median: 103
- standard deviation: 56.22
- interquartile range: 31.5
Sample Response
Reasons for each bowler:
- Although Person A has a low mean score, the large variability of scores indicates that this person can score well sometimes. This person’s scores are spread out, and it is not rare for this person to score over 140.
- Person B is very consistent. Although this person does not have great games like the other players, Person B’s mean score is near the top, and this person will reliably get a score between 120 and 160.
- Person C has a high mean score but has scores that are also really variable. This person had the lowest score in this group but has the greatest median score. I think we could coach this person to be more consistent, so this wild card could be on my team.
- Person D has the lowest mean, but is also capable of bowling a near perfect game (twice). This person had two games with scores that were much greater than anyone else’s on the list, so maybe Person D does well when it counts.
Activity Synthesis (Teacher Notes)
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 give reasons why another team may want this player on their team. If time allows, ask if there is any additional information that might make that player more desirable. For example, knowing the conditions behind each score might be helpful. Player C might be a new bowler, and the lower scores might have been when Player C was learning, but the newer scores may all be closer to 200. Player D might not take practice seriously, but can bowl a perfect game in competition.
Because there is no single correct answer, attend to students’ explanations, and ensure that the reasons given are correct. During the discussion, ask students to explain how they used the statistics given as well as the histograms.
Standards
- HSS-ID.A.1·Represent data with plots on the real number line (dot plots, histograms, and box plots).
- S-ID.1·Represent data with plots on the real number line (dot plots, histograms, and box plots).
- S-ID.1·Represent data with plots on the real number line (dot plots, histograms, and box plots).
- S-ID.1·Represent data with plots on the real number line (dot plots, histograms, and box plots).
- 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.