Comparing Mean and Median
5 min
Teacher Prep
Setup
Narrative
In this Warm-up, students review ways to interpret and compare data shown on a dot plot. The discussion on each given statement gives the teacher an opportunity to hear how students reason about the median, mean, typical value, spread, balance point, and MAD. This discussion will be helpful in upcoming activities, as students compare median and mean values for different data sets.
Launch
Give students 2 minutes of quiet work time. Follow with a whole-class discussion.
Student Task
Here are two dot plots. The first dot plot shows the heights of the first 22 U.S. presidents. The second dot plot shows the heights of the next 22 presidents.
Based on the two dot plots, decide if you agree or disagree with each of the following statements. Be prepared to explain your reasoning.
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The median height of the first 22 presidents is 178 centimeters.
-
The mean height of the first 22 presidents is about 183 centimeters.
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A typical height for a president in the second group is about 182 centimeters.
-
U.S. presidents have become taller over time.
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The heights of the first 22 presidents are more alike than the heights of the second 22 presidents.
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The MAD of the second data set is greater than the MAD of the first set.
Sample Response
- Agree. The median is the average of 178 and 178 centimeters, which are the 11th and 12th data points.
- Disagree. Though there are 4 presidents who are 183 centimeters tall, 183 is not the balance point of the data. There are many more presidents who are shorter than 183 centimeters than are taller than 183 centimeters.
- Agree. The center of the data appears to be about 182 centimeters.
- Agree. The center of the data in the second group is higher than in the first group.
- Disagree. The spread of the data for the first 22 presidents is wider than that for the other group, so overall their heights are more different.
- Disagree. Compared to the first group, the data points for the second group are clustered closer together, so their average distance from the mean is likely smaller, not greater.
Activity Synthesis (Teacher Notes)
For each statement, ask students to indicate if they agree or disagree. If all students agree or all students disagree, ask a couple of students to explain their reasoning. If the class is divided on a statement, ask students on both sides to share their reasoning until the class comes to an agreement. As students share, record and display their responses for all to see. If possible, record their reasoning on the dot plots to highlight important terms that students use.
To help facilitate the discussion, consider asking:
- “Who can restate ___’s reasoning in a different way?”
- “Did anyone have the same reasoning but would explain it differently?”
- “Did anyone reason about the statement in a different way?”
- “Does anyone want to add on to _____’s reasoning?”
- “Do you agree or disagree? Why?”
Standards
- 6.SP.5.b·Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
- 6.SP.5.c·Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
- 6.SP.B.5.b·Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
- 6.SP.B.5.c·Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
10 min
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Comparing Mean and Median
5 min
Teacher Prep
Setup
Narrative
In this Warm-up, students review ways to interpret and compare data shown on a dot plot. The discussion on each given statement gives the teacher an opportunity to hear how students reason about the median, mean, typical value, spread, balance point, and MAD. This discussion will be helpful in upcoming activities, as students compare median and mean values for different data sets.
Launch
Give students 2 minutes of quiet work time. Follow with a whole-class discussion.
Student Task
Here are two dot plots. The first dot plot shows the heights of the first 22 U.S. presidents. The second dot plot shows the heights of the next 22 presidents.
Based on the two dot plots, decide if you agree or disagree with each of the following statements. Be prepared to explain your reasoning.
-
The median height of the first 22 presidents is 178 centimeters.
-
The mean height of the first 22 presidents is about 183 centimeters.
-
A typical height for a president in the second group is about 182 centimeters.
-
U.S. presidents have become taller over time.
-
The heights of the first 22 presidents are more alike than the heights of the second 22 presidents.
-
The MAD of the second data set is greater than the MAD of the first set.
Sample Response
- Agree. The median is the average of 178 and 178 centimeters, which are the 11th and 12th data points.
- Disagree. Though there are 4 presidents who are 183 centimeters tall, 183 is not the balance point of the data. There are many more presidents who are shorter than 183 centimeters than are taller than 183 centimeters.
- Agree. The center of the data appears to be about 182 centimeters.
- Agree. The center of the data in the second group is higher than in the first group.
- Disagree. The spread of the data for the first 22 presidents is wider than that for the other group, so overall their heights are more different.
- Disagree. Compared to the first group, the data points for the second group are clustered closer together, so their average distance from the mean is likely smaller, not greater.
Activity Synthesis (Teacher Notes)
For each statement, ask students to indicate if they agree or disagree. If all students agree or all students disagree, ask a couple of students to explain their reasoning. If the class is divided on a statement, ask students on both sides to share their reasoning until the class comes to an agreement. As students share, record and display their responses for all to see. If possible, record their reasoning on the dot plots to highlight important terms that students use.
To help facilitate the discussion, consider asking:
- “Who can restate ___’s reasoning in a different way?”
- “Did anyone have the same reasoning but would explain it differently?”
- “Did anyone reason about the statement in a different way?”
- “Does anyone want to add on to _____’s reasoning?”
- “Do you agree or disagree? Why?”
Standards
- 6.SP.5.b·Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
- 6.SP.5.c·Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
- 6.SP.B.5.b·Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
- 6.SP.B.5.c·Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.