Utah Core State Standards Workshop 7Th Grade

Utah Core State Standards Workshop – 7th grade Statistics and Probability – 7SP.3 measures of central tendency – Learning Cycle Tony Anderson, Trisha Nef, Alicia Francom Statistics

Objective: Students will be able to find and understand the meaning of different measures of center and variation.

Develop Understanding Task:

The task of deciding which of the teams is taller uses data that was chosen so that the median of one team is greater while the mean of the other team is greater. Students can argue logically that either team is taller depending on how they use the statistics. This provides a nice launching point for a discussion on the different measures of central tendency.

Anticipated student work:  Some may notice that if the players from each team are lined up face-to-face in order of height, that the Bulls players are more often taller.  Using the mean, the Bulls are taller.  Using the median, the Jazz are taller.  Some may be very familiar with each team’s starting line-up and may compare only those 5 players’ heights.  The interquartile ranges are equivalent, but the mean abs. deviation for the Jazz is smaller. This means that all of the Jazz players are closer to the mean height than the Bulls are. There is no truly correct answer to this question (either team can be backed up by viable arguments), but we hope the relevant math comes to the surface and can be discussed in real world contexts so students better understand what it is they are finding.

Mea Media Mean Abs. n n Mode Interquartile Range Deviation Jazz 78.46 80 80 6.5 2.89 Bulls 78.62 79 81 6.5 3.15

Solidify Understanding Task:

For #1, if you teach at an ASD junior high, here is some data: Timberline – 29, Oak Canyon – 21, Lehi Jr. – 33, Willowcreek – 27, Lakeridge – 26, AF – 32, Orem – 22, PG – 29.

This question may be hard for students to process, so we would give them a specific time to do just number 1, then we would discuss it before letting them move on to the ‘easier’ questions.

Anticipate #1:  Students will feel as though this number is too low based on their own classes.  For part D if students need prompting, point out that the data is # of adults, not necessarily number of teachers. We will eventually tell them that when this calculation was made, they counted ALL the adults in the school including administrators, custodians and lunch ladies. Anticipate #2:  Ideally students can get through this on their own  We want them to see that the mean will be more drastically effected by Oprah than the median Anticipate #3  Students will probably think that the advertisement is accurate because the math is correct  Hopefully some students think they will be disappointed at the park because overall the coasters aren’t very tall, they just have one that is super tall. Anticipate #4  This will probably be more of a class discussion question

Practice Understanding Task:

The students will be given an assignment which allows them to conduct their own surveys. The students will need to come up with an appropriate question to ask, determine an unbiased sample population, and conduct the survey. With their data the students will need to make a visual that accurately reflects their data. After this, the students will find all of the appropriate measures of center and variation which will help them analyze their data. Students will need to write up a few paragraphs that explain what the measures of center and variation tell us about their population.

This practice task will allow students to connect all of the different skills we will be teaching them this unit. From graphing to calculating centers to analyzing their data, this should encompass many facets the students need to master.

In anticipation of this activity, students may at first select a question that would not work. For example, their question could be too misleading or vague. The teacher would need to monitor the creation of these questions, so have enough time in class to write the question before they leave, if this is used as homework. The same problems could easily arise with the sample population. The students need to survey the right people as feasible to their lives. Name ______Date ______Period______

Which Team is Taller?

Below are the actual heights (in inches) of players on the Utah Jazz and the Chicago Bulls. Which team is taller? Justify your answers in at least two ways.

Utah Jazz Chicago Bulls Name Height in inches Name Height in inches Earl Watson 73 John Lucas III 71 Blake Aheam 74 Mike James 74 Devin Harris 75 CJ Watson 74 Jamaal Tinsley 75 Derrick Rose 75 Raja Bell 77 Ronnie Brewer 79 Josh Howard 78 Richard Hamilton 79 Paul Millsap 80 Kyle Korver 79 Gordon Hayward 80 Carlos Boozer 81 DeMarre Carroll 80 Luol Deng 81 Jeremy Evans 81 Taj Gibson 81 Derrick Favors 82 Brian Scalabrine 81 Al Jefferson 82 Joakim Noah 83 Enes Canter 83 Omer Asik 84 Name ______Date ______Period ______

More Stats

1. Mrs. Nef looked up the average class size at Mountain Ridge Junior High on the internet and found out it was 27.

a. Do you think that is accurate? Why or why not?

b. Using an estimate of each of your classes, calculate your average class size here at MRJH.

c. Is your estimate close to 27? Why do you think this is?

d. Current data telling the number of adults and the number of students at our school was used and the website correctly calculates averages, yet they got 27. How do you think they could have gotten this number?

2. Here is some data of the annual income in a certain neighborhood, Holly Hills:

Neighbor Salary (per year) Mr. Rogers $40,000 Holly Hobby $55,000 Mr. Bean $48,000 Oscar the Grouch $20,000 Oprah Winfrey $50,450,000 a. Calculate the mean and the median

b. What does the mean tell you about the income in Holly Hills?

c. What does the median tell you about the income in Holly Hills?

d. Which do you think is a more accurate measure of center in this case, the mean or the median? Why? 3. A nearby amusement park recently boasted that their average roller coaster is 170 feet tall.

a. Is this an accurate advertisement?

b. If you went to this amusement park because you really like tall roller coasters, do you think you’d be disappointed? Why or why not?

4. How does an introduced outlier affect the mean/median?

Name ______Date ______Period ______

Vocabulary Reference Sheet

Term Definition Process What it tells you Example Mean

Median

Range Interquartile Range

Mean Abs. Deviation

Outlier Name ______Date ______Period ______

Your Statistical Experience

This is your opportunity to conduct a survey of your choice! Read the directions carefully!!!

Directions and work space:

1) Choose a question to ask a sample population. Be sure to structure the question so that the answers give you the data you want. Remember your data needs to be numerical! It would be a good idea to check your question with others.

2) Choose a sample population that would accurately reflect the population you are interested in. Remember all the things we have discussed. You do not want a biased sample. Below write down what your sample is and how you chose it.

3) Conduct your survey. Come up with a way to keep track of your data. Record below or on a separate piece of paper. 4) Organize/graph data. How do you want to present what you have found to an audience? Make sure your graph shows what you want to present to the audience. You may attach a separate paper if you want to use a computer or graph paper.

5) Analyze your data. Find centers and variations and explain which ones are the best measures for the given situation. Explain how you know your measures accurately reflect what you are researching.

6) Summarize your findings (this should answer your initial survey question).