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.
Jazz
Bulls
Mean Median Mode
78.46
80
80
78.62
79
81
Interquartile Range
6.5
6.5
Mean Abs.
Deviation
2.89
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
Name
Height in inches
Earl Watson
73
Blake Aheam
74
Devin Harris
75
Jamaal Tinsley
75
Raja Bell
77
Josh Howard
78
Paul Millsap
80
Gordon Hayward
80
DeMarre Carroll
80
Jeremy Evans
81
Derrick Favors
82
Al Jefferson
82
Enes Canter
83
Chicago Bulls
Name
Height in inches
John Lucas III
71
Mike James
74
CJ Watson
74
Derrick Rose
75
Ronnie Brewer
79
Richard Hamilton
79
Kyle Korver
79
Carlos Boozer
81
Luol Deng
81
Taj Gibson
81
Brian Scalabrine
81
Joakim Noah
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
Mean
Median
Mode
Range
Interquartile
Range
Mean Abs.
Deviation
Outlier
Definition
Process
What it tells you
Example
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).