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# Comparing Distributions

Lesson 2 of 11

## Objective: SWBAT interpret line plots and stem-and-leaf plots and use them to compare data.

Students enter silently according to the Daily Entrance Routine.. A timer is set at the front with the message:

Finish the “VOCAB” part of the Do Now in 3 minutes or less to earn an achievement point!

I am walking around the room with stickers in hand during these 3 minutes, awarding students their achievement points if they finished on time. I am also showing students which answers are incorrect. The answers are:

**(population)**an entire group of people or objects that researchers collect data about in order to study them**(random sample)**a small set that is representative of the larger population**(inference)**to make a prediction about a population based on the data collected**(measure of central tendency)**the central value that describes the distribution of the data

At the end of three minutes I review the answers with all students. I check for understanding asking for thumbs up, in the middle, or down for students’ comfort/level of understanding of each of the terms. It is important that students can identify the definitions of these words as I use them to communicate the big ideas behind representative samples. Notice bold words which may need to be further defined for students:

- Big Idea 1: Random samples need to be
**representative**in order to get**valid**results.**Valid**results are needed to make the correct**inference**, or prediction.

- Big Idea 2:
**Representative**samples accurately reflect the population. For example, if I want to throw a party for middle school students and need to find out their favorite food, I should NOT**survey**the teachers or elementary school students.

I provide 2 – 3 different examples for students like the one above, asking each time, why is a particular sample **reliable** or not? Why would/wouldn’t our results be **valid**?

This should only take about 5 minutes. The last five minutes of this section need to be devoted to students answering the multiple choice questions provided at the end of the Do Now. This is the final check for understanding and covers the standard 7.SP.1. Students may be given 2 minutes to review and **justify** their answers, giving them an opportunity to exercise **MP3** As they defend their answers and critique their peers answers and justifications. It may be necessary to give students an example of how one would justify their answer, for example, “Anissa should survey students at the middle school because this group of students represents her group of friends better than the elementary school kids”.

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After reviewing answers to the Do Now students are asked to put their papers away. They receive a guided practice + notes worksheet and must fill out the heading. I will take 5 – 6 minutes modeling how I think through the comparison between the two line plots in the 1^{st} given problem. Here are the essential ideas I am pointing out:

- Before comparing, be sure to understand what each x represents on the line plot.
- Each x represents a day for that vehicle. The owner of each vehicle measured the number of miles he was able to travel per gallon that day. Check for understanding by asking questions:
- How many days did the owners of the vehicle collect data?

- How many days did the owners of the vehicle collect data?

- Each x represents a day for that vehicle. The owner of each vehicle measured the number of miles he was able to travel per gallon that day. Check for understanding by asking questions:
- Begin by comparing the overall look of the line plot. What do you notice?
- There is a lot more “clumping” along the lower numbers of the left-side line plot. This means fewer miles per gallon. We can also say the data is “skewed to the left”
- The line plot on the right seems to have points that are more spread out and “symmetric” (students may need further explanation about what this means)

- Tell students that SUVs are less efficient than small cars because they can go shorter distances on the same amount of gasoline than small cars. With this information, students should be able to turn to their neighbors and determine which line plot shows the SUV and which shows the small car. Again, this is a great opportunity to practice
**MP3**.

After students have had an opportunity to discuss with their neighbor, we share out our answers and all students are given 5 minutes on a timer to write a summary of the discussion on the lines for this problem.

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A timer will again be set for 10 minutes. Students must independently and silently complete the second example in the worksheet given in the previous section. If finished early they must raise their hand. I will come by to check their work, asking them to consider and make any necessary changes. If finished early, students who have all or most of the work correct will be allowed to sit in booths with partners to review their answers. At the end of 10 minutes, all students will be asked to review their answers with neighbors. Students who are significantly behind in completing the work will need to review with me in a group.

A common misconception in this lesson is misreading the stem and leaf plot. Some students will still need lots of scaffolding for understanding that each value is a price for a DVD. For these students it is often necessary to point at a common paper, showing them how to put together the stem and the leaf to understand the problem.

In the last 3 minutes of this section all students will be asked to pick up a clicker from the back of the room and return to their seats.

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#### Closing

*10 min*

In the closing section of class students will be asked to answer two questions and enter the answers into clickers.

**Yes / No**Would you be interested in reviewing today’s lesson once more during study hall/remediation? Select yes if you still do not feel comfortable with this topic!

- Games Unlimited buys video games for $10. The store increases their purchase price by 300%. What is the sales price of the video game?
**A.**$20**B.**$30**C.**$40**D.**$50

I will be taking these results and using them to determine which students continue to need remediation on the topics of random sampling, comparing distributions, and percent change. Students will be allowed to work for 5 minutes silently and we will have time to review the answer to the second question. Some students may still need additional help.

At the end of class homework is distribute and students are dismissed for their next class.

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- UNIT 1: Integers
- UNIT 2: Operations with Rational Numbers
- UNIT 3: Expressions and Equations - The Basics
- UNIT 4: Multi-step Equations, Inequalities, and Factoring
- UNIT 5: Ratios and Proportional Relationships
- UNIT 6: Percent Applications
- UNIT 7: Statistics and Probability
- UNIT 8: Test Prep
- UNIT 9: Geometry

- LESSON 1: Central Tendency
- LESSON 2: Comparing Distributions
- LESSON 3: Line plot & Stem-and-Leaf Plot
- LESSON 4: Comparing Distributions Part II
- LESSON 5: Variability
- LESSON 6: Measures of Variation - Range and IQR
- LESSON 7: Box and Whisker Plots
- LESSON 8: Mean Absolute Deviation
- LESSON 9: Quiz + The Language of Probability
- LESSON 10: Theoretical vs Experimental Probabilities
- LESSON 11: Compound Probability