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K12MATH006: Math Grade 6

Unit 6: Statistics  

Newspapers, television commentators, politicians, and sports commentators talk about statistics all the time. This will be your opportunity to really understand the numbers they are referencing and make your own judgments and conclusions. Statistics have a range of ways they can be interpreted, and you want to make sure you are active in your own learning from these various sources. During this unit, you will learn some differences between measures of center and how data varies. You will also learn about how data distributed on a graph can tell viewers a lot about what they are seeing if they look closely enough. Many people say “numbers don’t lie,” but don’t forget, it is your job to make sure you are getting the truth about the numbers.

Unit 6 Time Advisory
Completing this unit should take you approximately 6 hours and 15 minutes.

☐ Subunit 6.1: 30 minutes

☐ Subunit 6.2: 30 minutes

☐ Subunit 6.3: 1 hour and 15 minutes

☐ Subunit 6.4: 4 hours

Unit6 Learning Outcomes
Upon successful completion of this unit, the student will be able to:

  • Identify a statistical question that will anticipate variability in the data.

  • Explain how the measures of center represent a set of data.

  • Compare and contrast the difference between measures of center and a measure of variation.

  • Visually summarize a set of data using box plots, dot plots, and histograms.

  • Write and explain the context of a set of data using both qualitative and quantitative information.

Standards Addressed (Common Core):

6.1 Measures of Center  

In the 2013 NBA Playoff, Miami Heat star player LeBron James had 25.9 PPG (points per game). Most people, whether they are basketball fans or not, can probably tell you that it is not possible to score 0.9 of a point in a basketball game. So where did this number come from? Sports statistics are an example of taking a set of data and using a measure of center to describe the data set with one number. In this subunit, you will learn about three specific measures of center - mean, median, and mode. These might already be familiar to you; however, you will also learn about the importance of when to use, and not use, each of these specific measurements. In the case of LeBron James, the mean was used to calculate the average points he scored in all the NBA playoff games. 

  • Explanation: YouTube: Mathispower4u: James Sousa’s “Mean, Median, and Mode”

    Link: YouTube: Mathispower4u: James Sousa’s “Mean, Median, and Mode” (YouTube)

    Instructions: As you watch the video, take notes of the definitions for mean, median, and mode. Do the example problems with the instructor. Take the time to write out all the data points and solve for each measure of center. Pay extra-close attention at about the 6:10 point in the video when the instructor begins talking about why it’s important to have multiple measures of center. He introduces the word outlier and then goes on to show a really informative animation about how changing one value can have different effects on the data.

    Watching the video and taking notes should take you approximately 15 minutes.

    Standards Addressed (Common Core):

    Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License. It is attributed to James Sousa.

  • Explanation: LearnZillion: Jennifer Rising’s “Summarize the Center of Data with a Single Number Using Mean, Median, and Mode”

    Link: LearnZillion: Jennifer Rising’s “Summarize the Center of Data with a Single Number Using Mean, Median, and Mode” (Flash)

    Instructions: The purpose of this video is to help you figure out which measure of center is best for a specific set of data. As you watch, solve for each mean, median, and mode with the instructor. Think about which measure of center would best summarize the data. Then pay attention to the explanation the instructor gives as to which measure of center best represents the data.

    Watching this video should take you approximately 15 minutes.

    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

6.2 Statistical Questioning  

A statistical question is one that accounts for variability. For example, if you were asked, “How old are you?” there is only one answer - no variability. However, if you were asked, “How old are all the kids in your neighborhood?” then one could anticipate variability in ages. Therefore, “How old are all the kids in your neighborhood?” is a statistical question.

Consider the question: “Who was the first president of the United States?” This is not a statistical question because there is only one answer. There is no variability in the answer.

Consider the question: “How tall are the roller coasters at Cedar Point Amusement Park?” This question would result in a variety of answer because there are multiple roller coasters that have variability in their heights. This means this is a statistical question.

  • Did I Get This? Activity: Illustrative Mathematics: “Buttons: Statistical Questions”

    Link: Illustrative Mathematics: “Buttons: Statistical Questions” (HTML)

    Instructions: Read about Zeke and his button collection on the first page. Answer both question a and b. Notice question a asks you to explain whether each question is or is not a statistical question.

    Read the commentary on the top of the second page. It is a very informative explanation about statistical questions. Check your answers and read the solution explanation on pages two and three.

    Completing this activity should take you approximately 30 minutes.

    Standards Addressed (Common Core):

    Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

6.3 Statistical Variability  

Numbers are everywhere. We often look at surveys or statistics and make conclusions about situations. Perhaps you have looked at temperatures for an upcoming vacation destination to know what kind of clothes to pack in your suitcase. If the temperatures have a wide range of variability, then you might end up packing lots of clothes so you are prepared for the different temperatures! As you work through this subunit you will learn a few different ways to measure variability.

6.3.1 Interquartile Range   - Explanation: CK-12: “Quartiles”

Link: CK-12:
[“Quartiles”](http://www.ck12.org/statistics/Quartiles/lesson/Quartiles/) (HTML)

Instructions: The purpose of this resource is to learn about how
find a quartile within a set of data. You will only be using part of
this resource to gather information. Read the “Guidance” section,
and take notes on how to find the median, lower quartile, and upper
quartile. You will use these words in the next resource, and again
in subunit 6.4 when you make a box plot. Add the words from the
“Vocabulary” section to your notes.

Reading this lesson and taking notes should take you approximately
15 minutes.

Standards Addressed (*Common Core*):

-   [CCSS.Math.Content.6.SP.A.2](http://www.corestandards.org/Math/Content/6/SP/A/2)
-   [CCSS.Math.Content.6.SP.A.3](http://www.corestandards.org/Math/Content/6/SP/A/3)
-   [CCSS.Math.Content.6.SP.B.5.c](http://www.corestandards.org/Math/Content/6/SP/B/5/c)

Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial 3.0 Unported
License](http://creativecommons.org/licenses/by-nc/3.0/). It is
attributed to CK-12.
  • Explanation: CK-12: “Measures of Spread”

    Link: CK-12: “Measures of Spread” (HTML)

    Instructions: Read the introduction to learn about measures of dispersion. Although it is a review, read about range and take any additional notes you might find helpful.

    Take notes as you read about the interquartile range (IQR). Remember that to find the different quartiles, you must use the median of the entire data; then the median of the first half of the data = lower quartile = Q1; and finally the median of the second half of the data = upper quartile = Q3.

    Read about why the IQR is important and when is it used. Complete the exercises in the “Review Questions” section.

    Reading this lesson, taking notes, and completing the example problems should take you approximately 30 minutes.

    Standards Addressed (Common Core):

    Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License. It is attributed to CK-12.

6.3.2 Mean Absolute Deviation   - Web Media: CK-12: “Data Analysis Using Dot Plots, Measures of Central Tendency, and Interquartile Range - 7.SP.3,4” Link: CK-12: “Data Analysis Using Dot Plots, Measures of Central Tendency, and Interquartile Range -7.SP.3,4” (HTML)

 Instructions: Scroll about halfway down the page until you see the
section titled “Mean Absolute Deviation.” Read through the text and
the first example that results in a mean absolute deviation of 3.75.
Read through the same section one more time, taking notes and
solving the problem step-by-step. Look at the next example with the
two teams. Try solving for the mean and then the mean absolute
deviation on your own. Scroll down to check your work or to get a
hint for the next steps in solving the problem. Take notes on the
final paragraph that explains what the mean absolute deviation
represents for a data set. At the end of this paragraph, follow the
second link, which leads to a video that shows another example of
finding the mean absolute deviation. As you watch the video, pause
it when the instructor gives you the data points, solve for the mean
absolute deviation, and then watch the remainder of the video to
check your work. Note: The section prior to the information on mean
absolute deviation is “Measures of Central Tendency,” and the
section following the information on mean absolute deviation is
“Interquartile Range.” If you want additional information about
either of these two concepts, review them at this time. Taking
notes, completing the examples, and watching the video should take
you approximately 45 minutes.   

 Standards Addressed (*Common Core*):

-   [CCSS.Math.Content.6.SP.A.2](http://www.corestandards.org/Math/Content/6/SP/A/2)
-   [CCSS.Math.Content.6.SP.A.3](http://www.corestandards.org/Math/Content/6/SP/A/3)
-   [CCSS.Math.Content.6.SP.B.5.c](http://www.corestandards.org/Math/Content/6/SP/B/5/c)

Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial 3.0 Unported
License](http://creativecommons.org/licenses/by-nc/3.0/). It is
attributed to CK-12.
  • Explanation: YouTube: Tony Baker’s “Mean Absolute Deviation”

    Link: YouTube: Tony Baker’s “Mean Absolute Deviation” (YouTube)

    Instructions: Watch the video and take notes of how to find the mean absolute deviation (MAD). Write down each step and then solve for the MAD with the instructor. At the 1:43 mark, take notes as the instructor explains what the value MAD means in terms of variability as it compares to zero.

    Watching this video and taking notes should take you approximately 15 minutes.

    Standards Addressed (Common Core):

    Terms of Use: This resource is licensed under a Creative Commons Attribution 3.0 Unported License.

  • Explanation: LearnZillion: Jennifer Rising’s “Summarize the Set of Data Using Range and Mean Absolute Deviation”

    Link: LearnZillion: Jennifer Rising’s “Summarize the Set of Data Using Range and Mean Absolute Deviation” (Flash)

    Instructions: This video shows that a measure of variability can be broken down into one single number, much like a measure of center can. As you watch the video, take notes about not only how to find range and mean absolute deviation, but also what their values mean in terms of the variability of the data set.

    Write a paragraph that compares and contrasts mean to mean absolute deviation. Give more than just the definition of each - explain how to solve for each, when they are used, what each number tells you in general about the set of data. Spend some time looking at your own world for a situation where you might use each of these statistical measurements.

    Watching the video and taking notes should take you approximately 15 minutes.

    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

6.4 Summarizing Data Sets  

Have you ever been given a bunch of data and asked to summarize what it all means? Perhaps you saw in the local newspaper the daily temperatures from the last month. Trying to make sense of 30 temperatures can get confusing if you don’t have a way to display the data. In this subunit you will learn about three ways to display data - dot plots, histograms, and box plots. You will also learn about how to describe the shape of the graph and what the shape tells you about the data set in general. You probably have some experience with other types of graphs. As you work this subunit, use your prior knowledge to compare and contrast the other types of graphs you already know about to the ones you will make here. 

  • Explanation: LearnZillion: Jennifer Rising’s “Analyze the Shape of a Graph to Describe the Distribution of Data”

    Link: LearnZillion: Jennifer Rising’s “Analyze the Shape of a Graph to Describe the Distribution of Data” (Flash)

    Instructions: As you watch the video, pause it to do a quick sketch and label of each graph example. This allows you to have a visual in your notebook of each of the graphs mentioned in the video. It is important that you feel confident with how to explain a graph’s overall shape in mathematical terms.

    Watching the video and taking notes should take you approximately 15 minutes.

    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

6.4.1 Histograms   - Explanation: YouTube: Mathispower4u: James Sousa’s “Histogram”

Link: YouTube: Mathispower4u: James Sousa’s
[“Histogram”](http://www.youtube.com/watch?v=RWP2q4wyRds&feature=youtu.be) (YouTube)

Instructions: While you watch the video, make the histogram with the
instructor. Do all parts of the process to help you understand how
to find the frequency and the intervals. Make sure your final
product looks the same as the instructor’s. Notice there are labels
for the axis as well as a title. Do not forget these important parts
of a graph!

Watching the video and taking notes should take you approximately 15
minutes.

Standards Addressed (*Common Core)*:

-   [CCSS.Math.Content.6.SP.B.4](http://www.corestandards.org/Math/Content/6/SP/B/4)

Terms of Use: This resource is licensed under a [Creative Commons
Attribution 3.0 Unported
License](http://creativecommons.org/licenses/by/3.0/). It is
attributed to James Sousa.
  • Explanation: CK-12: “Frequency Tables and Histograms”

    Link: CK-12: “Frequency Tables and Histograms” (HTML)

    Instructions: Read about the boys on the track team and their heights. Read the “Guidance” section and take notes about the word frequency and note how to make a frequency table. Continue reading about histograms. You are probably familiar with a bar graph. Notice that with a histogram there can be an interval of numbers on the horizontal axis, and there is also no space in between the bars of data.

    Go through each of the true/false example questions and check your solutions. Use the frequency table already made for you to make a histogram to represent the heights of the boys from each team. Notice how you can use wider intervals and have two bars of different colors to separate the schools. This is called a double histogram.

    In your notebook, copy the words from the “Vocabulary” section. Complete the “Guided Practice” problem in your notebook and check your solution. Skip the video. Complete questions 1 - 3 from the “Practice” section.

    Reading this lesson, taking notes, and completing the practice problems should take you approximately 45 minutes.

    Standards Addressed (Common Core):

    Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License. It is attributed to CK-12.

6.4.2 Dot Plots   - Explanation: CK-12: “Line Plots from Frequency Tables”

Link: CK-12: [“Line Plots from Frequency
Tables”](http://www.ck12.org/statistics/Line-Plots-from-Frequency-Tables/lesson/Line-Plots-from-Frequency-Tables/) (HTML)

Instructions: Look at the frequency table representing workers in
the garden. You will learn about how to take this data and make a
line plot, also called a dot plot. Read about line plots in the
“Guidance” section. Take notes about how to make a line plot and
when they are commonly used.

Using the line plot that is already completed and represents the
number of students per class, answer the example questions and check
your solutions.

Write down the vocabulary words in your notebook. Complete the
“Guided Practice” section and check your solution. Skip the video
and complete questions 1 - 11 in the “Practice” section.

Reading this lesson, taking notes, and completing the examples
should take you approximately 45 minutes.

Standards Addressed (*Common Core*):

-   [CCSS.Math.Content.6.SP.B.4](http://www.corestandards.org/Math/Content/6/SP/B/4)
-   [CCSS.Math.Content.6.SP.B.5.c](http://www.corestandards.org/Math/Content/6/SP/B/5/c)

Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial 3.0 Unported
License](http://creativecommons.org/licenses/by-nc/3.0/). It is
attributed to CK-12.

6.4.3 Box Plots   - Explanation: Khan Academy’s “Box-and-Whisker Plot”

Link: Khan Academy’s [“Box-and-Whisker
Plot”](https://www.khanacademy.org/math/probability/descriptive-statistics/Box-and-whisker%20plots/v/box-and-whisker-plots) (YouTube)

Instructions: Watch the video and listen to how to begin making a
box plot (also called box-and-whisker). At the 4:34 mark, the
instructor introduces the word quartile. Note that there are four
quartiles (think four quarters). You will use quartiles to set up
the box plot. As you work, notice you are using the median
throughout the data. Continue following along with the instructor to
make the box plot.

Watching this video and taking notes should take you approximately
15 minutes.

Standards Addressed (*Common Core*):

-   [CCSS.Math.Content.6.SP.B.4](http://www.corestandards.org/Math/Content/6/SP/B/4)

Terms of Use: This resource is licensed under a [Creative Commons
Attribution-NonCommercial-NoDerivs 3.0 Unported
License](http://creativecommons.org/licenses/by-nc-nd/3.0/). It is
attributed to the Khan Academy.
  • Explanation: Khan Academy’s “Reading Box-and-Whisker Plots”

    Link: Khan Academy’s “Reading Box-and-Whisker Plots” (YouTube)

    Instructions: Draw a sketch of the box plot shown in the video. Label the median with the instructor at the 1:25 mark. Continue to label the quartiles as the instructor explains them. Make sure you know how to find the range, median, and each quartile when looking at a completed box plot

    Watching this video and taking notes should take you approximately 15 minutes.

    Standards Addressed (Common Core):

    Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. It is attributed to the Khan Academy.

  • Did I Get This? Activity: Khan Academy’s “Creating Box and Whisker Plots”

    Link: Khan Academy’s “Creating Box and Whisker Plots” (YouTube)

    Instructions: This page provides a series of practice problems that you can answer and check online. Each question has a solution worked out step-by-step if you need hints along the way. Practice creating box plots until you feel confident that you understand how to successful represent any set of data (recommended a minimum of 10 minutes of practice).

    Completing these practice problems should take you approximately 15 minutes.

    Standards Addressed (Common Core):

    Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. It is attributed to the Khan Academy.

  • Checkpoint: Illustrative Mathematics: “Puppy Weights” Link: Illustrative Mathematics: “Puppy Weights” (HTML)

    Instructions: Question a asks you to summarize the information using an appropriate graph. You should summarize the data using a dot plot, histogram, and box plot. Although it is not usually necessary to make three graphs of the same data, this is a good opportunity to show your ability to make these graphs.
    When you answer question b, you need to make sure you answer the question in complete detail. The question asks you to describe the shape (skewed), center (mean and median), and variability (interquartile range and mean absolute deviation).
    Check your solutions for a - c on pages two and three.
    Making the graphs, describing the data, and checking your solutions should take you approximately 30 minutes.

    Standards Addressed (Common Core):

    Terms of Use: This resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

6.4.4 Checkpoint   - Checkpoint: The Saylor Foundation’s “K12MATH006 Unit 6 Checkpoint” Link: The Saylor Foundation’s “K12MATH006 Unit 6 Checkpoint” (HTML)

 Instructions: Test your knowledge by completing this checkpoint.  

 Note: You must be logged into your Saylor Foundation School account
in order to access this checkpoint. If you do not yet have an
account, you will be able to create one, free of charge, after
clicking the link.

Final Exam   - Final Exam: The Saylor Foundation’s “K12MATH006 Final Exam” Link: The Saylor Foundation’s “K12MATH006 Final Exam” (HTML)

 Instructions: Complete this exam.  

 Note: You must be logged into your Saylor Foundation School account
in order to access this exam. If you do not yet have an account, you
will be able to create one, free of charge, after clicking the link.