## Engage NY Eureka Math Grade 6 Module 6 Lesson 21 Answer Key

### Eureka Math Grade 6 Module 6 Lesson 21 Exploratory Challenge Answer Key

Exploratory Challenge: Annual Rainfall in the State of New York

Question 1.

The National Climate Data Center collects data throughout the United States that can be used to summarize the climate of a region. You can obtain climate data for a state, a city, a county, or a region. If you were interested in researching the climate in your area, what data would you collect? Explain why you think these data would be important in a statistical study of the climate in your area.

Answer:

Answers will vary. Anticipate that student responses will include things like temperature, amount of rainfall, number of sunny days per year, number of tornadoes per year, etc.

For this lesson, you will use yearly rainfall data for the state of New York that were compiled the National Climate Data Center. The following data are the number of inches of rain (averaged over various locations in the state) for the years from 1983 to 2012 (30 years).

Use the four steps to carry out a statistical study using these data.

Step 1: Pose a question that can be answered by data.

What is a statistical question that you think can be answered with these data? Write your question in the template provided for this lesson.

Step 2: Collect appropriate data.

The data have already been collected for this lesson. How do you think these data were collected? Recall that the data are the number of inches of rain (averaged over various locations in the state) for the years from 1983 to 2012 (30 years). Write a summary of how you think the data were collected in the template for this lesson.

Step 3: Summarize the data with graphs and numerical summaries.

A good first step might be to summarize the data with a dot plot. What other graph might you construct? Construct a dot plot or another appropriate graph in the template for this lesson.

What numerical summaries will you calculate? What measure of center will you use to describe a typical value for these data? What measure of variability will you calculate and use to summarize the variability of the data? Calculate the numerical summaries, and write them in the template for this lesson.

Step 4: Answer your statistical question using the numerical summaries and graphs.

Write a summary that answers the question you posed in the template for this lesson.

### Eureka Math Grade 6 Module 6 Lesson 21 Template Answer Key

Template for Lesson 21

Step 1: Pose a question that can be answered by data.

What is a statistical question that you think can be answered with these data? Write your question in the template provided for this lesson.

It is important that students are reminded of the two most important parts of the definition of a statistical question. A statistical question is (1) a question that is answered by data and (2) a question that anticipates the data will vary. As students examine the data, point out to them that there is variability.

Although students may use different wording in their statistical questions, it is anticipated that most students will form a question that essentially asks, “What is the typical annual rainfall in New York?”

Step 2: How do you think the data were collected?

The data have already been collected for this lesson. How do you think these data were collected? Recall that the data are the number of inches of rain (averaged over various locations in the state) for the years from 1983 to 2012 (30 years). Write a summary of how you think the data were collected in the template for this lesson.

The data are provided in this lesson. This step is more challenging as they carry out their own statistical study because they need to explain the plan they developed to collect their data. For this lesson, allow students to speculate on how the National Climate Data Center might have collected these data.

As the data represent the annual rainfall for the state of New York, the center had to collect rainfall totals from several reporting weather centers around the state. They calculated an average of those levels for each day of the year. At the end of the year, the National Climate Data Center added those daily results together. Students might be asked how a rainfall level is measured at a weather center. A rain gauge might be a good visual to share with students.

Step 3: Construct graphs and calculate numerical summaries of the data.

1. A good first step might be to summarize the data with a dot plot. What other graph might you construct? Construct a dot plot or another appropriate graph in the template for this lesson.

2. What numerical summaries will you calculate? What measure of center will you use to describe a typical value for these data? What measure of variability will you calculate and use to summarize the variability of the data? Calculate the numerical summaries, and write them in the template for this lesson.

This step represents most of the work students are expected to do in this lesson. As a first step, encourage students who are not sure how to start summarizing the data to construct a dot plot. A blank grid is provided at the end of the Teacher Notes that can be duplicated for students who may need some structure in making a dot plot. This grid could also be used if any student decides to develop a box plot or a histogram of the data distribution.

Students examine the dot plot and make decisions about the data distribution. For example, is the distribution

approximately symmetric, or is the distribution skewed? This dot plot shows a data distribution that is approximately symmetric.

Based on the decision that the distribution is approximately symmetric, students should proceed to calculate the mean as a measure of center and the MAD as a measure of variability. Some students might also choose to investigate this distribution with a box plot to answer the question about the symmetry.

The box plot does not indicate a perfectly symmetrical distribution; however, it is approximately symmetric. The mean and the median of this data distribution are nearly equal to each other. Based on this decision, students should calculate the mean and the MAD.

The mean rainfall is 43 inches (to the nearest inch), and the mean absolute deviation (MAD) is 3.9 or 4 inches (to the nearest inch).

At the end of the Teacher Notes is a table that could be used for students who need structure in calculating the MAD. There are several steps in calculating the MAD, and some students may need help in organizing these steps.

Step 4: Answer your statistical question using the numerical summaries and graphs.

Write a summary that answers the question you posed in the template for this lesson.

This step asks students to write a short summary interpreting the graphs and numerical summaries. Students should connect this back to their statistical questions. Students would indicate that the typical rainfall for New York is about 43 inches per year. They would also indicate that a typical distance from the mean is about 4 inches.

### Eureka Math Grade 6 Module 6 Lesson 21 Problem Set Answer Key

In Lesson 17, you posed a statistical question and created a plan to collect data to answer your question. You also constructed graphs and calculated numerical summaries of your data. Review the data collected and your summaries.

Based on directions from your teacher, create a poster or an outline for a presentation using your own data. On your poster, indicate your statistical question. Also, indicate a brief summary of how you collected your data based on the plan you proposed in Lesson 17. Include a graph that shows the shape of the data distribution, along with summary measures of center and variability. Finally, answer your statistical question based on the graphs and the numerical summaries.

Share the poster you will present in Lesson 22 with your teacher. If you are instructed to prepare an outline of the presentation, share your outline with your teacher.

### Eureka Math Grade 6 Module 6 Lesson 21 Exit Ticket Answer Key

Question 1.

Based on the statistical question you are investigating for your project, summarize the four steps you are expected to complete as part of the presentation of your statistical study.

Answer:

Step 1:

State my statistical question. My question is based on collecting data that will vary.

Step 2:

Devise a plan to collect data. I prepared a question to ask the students in my class. (Allow students to explain the question they asked, the responses they received, and the method they used for recording answers.)

Step 3:

Summarize my data. I prepared a dot plot of the responses to the question. My dot plot indicated that the responses to my question were skewed to the left; therefore, I used the median of the data distribution to describe my center and the IQR to describe the variability. (Allow for a summary of the specific median or mean and a specific summary of the variability as the MAD or IQR.)

Step 4:

Based on my graphs and numerical summaries, I answered my question.