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Unit 8, Lesson 5: Using Dot Plots to Answer StatisticalQuestions

5.1: Packs on Backs (5 minutes)

Setup: Students in groups of 2. A couple of minutes of quiet work time, followed by partner and whole-class discussions.

Lesson GoalsDescribe the variability of values in the data set in terms of the center and spread.Understand that the center of a distribution can be used to describe the distributionusing a typical member of the population.Use dot plots to represent distributions and answer questions about the context.

Required Materials••

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GRADE 6 MATHEMATICS

Open Up Resources(openupresources.org)

Unit 8: Data Sets and Distributions, Lesson 5: Using Dot Plots to Answer Statistical Questions 1

Student task statementThis dot plot shows the weights of backpacks, in kilograms, of 50 sixth-grade students at a school in NewZealand.

1. The dot plot shows several dots at 0 kilograms. What could a value of 0 mean in this context?

2. Clare and Tyler studied the dot plot.

Clare said, “I think we can use 3 kilograms to describe a typical backpack weight of the groupbecause it represents 20%—or the largest portion—of the data.”

Tyler disagreed and said, “I think 3 kilograms is too low to describe a typical weight. Half of the dotsare for backpacks that are heavier than 3 kilograms, so I would use a larger value.”

Do you agree with either of them? Explain your reasoning.

Possible responses

1. Answers vary. Sample response: Avalue of 0 could representsstudents who don’t use backpacks.

2. Answers vary.

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GRADE 6 MATHEMATICS



5.2: On the Phone (15 minutes)

Setup:

Students in groups of 2. 5–6 minutes of quiet work time for the first 3 sets of questions, followed by 4–5 minutes of partner collaborationon the last 2 questions.

GRADE 6 MATHEMATICS



Student task statementTwenty-five sixth-grade students were asked to estimate how many hours a week they spend talking on thephone. This dot plot represents their reported number of hours of phone usage per week.

1. a. How many of the students reported not talking on the phone during the week? Explain how youknow.

b. What percentage of the students reported not talking on the phone?

2. a. What is the largest number of hours a student spent talking on the phone per week?

b. What percentage of the group reported talking on the phone for this amount of time?

3. a. How many hours would you say that these students typically spend talking on the phone?

b. How many minutes per day would that be?

4. a. How would you describe the spread of the data? Would you consider these students’ amounts oftime on the phone to be alike or different? Explain your reasoning.

b. Here is the dot plot from an earlier activity. It shows the number of hours per week the same groupof 25 sixth-grade students reported spending on homework.

Possible responses

1. A. Ten students, the number ofdots above 0; B. 40%.

2. A. 3 hours; B. 12%

3. Answers vary. Sample responses: A.about 1 hour per week; B. around 9minutes per day.

4. Answers vary. Sample response:a. The spread is pretty small. The

hours reported span from 0 to3, with a little more than half ofthe values being either 0 or 1,and the rest being 2 or 3.

b. The students are more alike intheir phone usage. The spreadof the data is much larger onthe homework time dot plot.

5. Answers vary.

GRADE 6 MATHEMATICS



Overall, are these students more alike in the amount of time they spend talking on the phone or inthe amount of time they spend on homework? Explain your reasoning.

5. Suppose someone claimed that these sixth-grade students spend too much time on the phone. Do youagree? Use your analysis of the dot plot to support your answer.

Anticipated misconceptions

Students may neglect to change therate given (from minutes per week tohours per week, or to minutes per day)and may draw incorrect conclusions asa result. Ask them to think aboutthe unit they are using in theirresponses.

GRADE 6 MATHEMATICS



5.3: Click-Clack (15 minutes)

Setup:

Students in groups of 2. 5–6 minutes of quiet work time for the first two questions, followed by 2–3 minutes of partner collaboration onthe last question.

GRADE 6 MATHEMATICS



Student task statement1. A keyboarding teacher wondered: “Do typing speeds of students improve after taking a keyboarding

course?” Explain why her question is a statistical question.

2. The teacher recorded the number of words that her students could type per minute at the beginning of acourse and again at the end. The two dot plots show the two data sets.

Based on the dot plots, do you agree with each of the following statements about this group of students?Be prepared to explain your reasoning.

a. Overall, the students’ typing speed did not improve. They typed at the same speed at the end of thecourse as they did at the beginning.

b. 20 words per minute is a good estimate for how fast, in general, the students typed at the beginningof the course.

c. 20 words per minute is a good description of the center of the data set at the end of the course.

d. There was more variability in the typing speeds at the beginning of the course than at the end, so

Possible responses

1. Data are needed to answer thequestion, and we can expect it tohave variability.

2. Answers vary. Sample response: A.Disagree; B. Agree; C. Disagree; D.Agree.

3. Answers vary. Sample response:about 26 words per minute

Anticipated misconceptions

Some students might find it challengingto tell where the center of a distributioncould be just by looking at a single dotplot. The idea of center might be moreapparent when presented incomparative terms. For example, askthem to describe in their own wordshow the distribution of the first dot plotdiffers from that of the second dot plot.Students are likely able to say that,compared to the first dot plot,the aggregation of dots in the second

GRADE 6 MATHEMATICS



Lesson Synthesis (5 minutes)What do we mean by the "center" and "spread" of a distribution? How do the center and spread of a distribution relate to a typicalmember of the group? How do we identify center and spread in a dot plot?

5.4: Packing Tomatoes (Cool-down, 5 minutes)

Setup: None.

the students’ typing speeds were more alike at the end.

3. Overall, how fast would you say that the students typed after completing the course? What would youconsider the center of the end-of-course data?

dot plot is overall higher on the numberline. Ask them if there is a location oneach dot plot around which data pointsseem to congregate.

Are you ready for more?Use one of these suggestions (or make up your own). Research to create a dot plot with at least 10 values.Then, describe the center and spread of the distribution.

Points scored by your favorite sports team in its last 10 gamesLength of your 10 favorite movies (in minutes)Ages of your favorite 10 celebrities

Possible Responses

Answers vary.

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GRADE 6 MATHEMATICS



Student task statementA farmer sells tomatoes in packages of ten. She would like the tomatoes in each package to all be about thesame size and close to 5.5 ounces in weight.

The farmer is considering two different tomato varieties: Variety A and Variety B. She weighs 25 tomatoes ofeach variety. These dot plots show her data.

1. What would be a good description for the weight of Variety A tomatoes, in general? What about for theweight of Variety B tomatoes, in general?

2. Which tomato variety should the farmer choose? Explain your reasoning.

Possible responses

1. In general, Variety A tomatoes areabout 5.49 ounces and Variety Btomatoes are about 5.5 ounces.

2. She should choose Variety B.Sample reasoning: There was muchless variation in Variety B tomato,so they're more likely to be thesame size and closer to 5.5 ounces.

GRADE 6 MATHEMATICS



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