Grade Level/Course: Grade 6 Lesson/Unit Plan Name: Statistical Questions and Variability Rationale/Lesson Abstract: Students design survey questions that anticipate variability. Students understand surveys measure a variety of responses with specific numerical answers. Timeframe: 1-­‐2 45 minute periods Common Core Standard(s): Develop understanding of statistical variability. 6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Page 1 of 9
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Instructional Resources/Materials: Warm-­‐up, Easel Pad or poster size paper, dot stickers Activity/Lesson (Day 1): Data analysis is at work all around us…
• Internet advertising
• Billboard placement
• Store location
• Traffic flow and road construction
• Carbon footprint
• Cell phone plans and rates
• Insurance
• Assessment data
In order to get any meaning or value from data, we need to make sure we are asking a question
that invites a certain amount of variability in order to provide a measurable and comparable data.
For example, the question, “How old are the students in my class in terms of years?” may
produce a graph as in figure A below. (Show the graph on overhead/projector)
Alternately, the question, “How old are the student in my class in terms of months?” may
produce a graph as in figure B below. (Show the graph in a side-by-side comparison with figure
A)
Figure A Figure B ASK: What do you notice when comparing the two graphs?
Sample Responses:
• The data in Figure B is more spread out.
• There are only three bars in Fig. A, and 13 bars on information in Fig. B.
• The same number of students are represented on both graphs but the data is more spread
out in Fig. B
• There is a gap in the data in Fig. B
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•
•
Fig. A tells us most students are 11-years-old, Fig. B tells us a higher concentration (or
cluster) of students are between 136 and 137 months old.
Fig. A tells us students range from 10-12 years old in this class (range = 2 years), Fig. B
tells us students range from 131-145 months old in this class (range = 14 months, a little
more than one year).
ASK: What conclusions can we draw from the table in Fig. A? Fig. B?
Sample Responses:
• Figure A: Most students are 11 years old.
• Figure B: No one in the class is 139 months old. The two oldest students are 145 months
old. The two youngest students are 131 months old. And so on…
BIG IDEA: The best survey questions provide data that invites and anticipates a certain amount
of variability.
Based on the two graphs above, notice how much a difference the question makes in the way the
data looks and the information it provides. Let’s consider a few questions that might be used for
a survey and determine how much variability each question invites.
DISCUSS/COMPARE/MODEL:
Use the following questions and discuss…
• Which question provides the most/least variability?
• What do we expect to find out from the data?
• What does the data reveal? What conclusions can we draw from the data?
• Do you exercise during the
• How much time do you
OR
week?
spend exercising per week?
• Do you have a Facebook
• How many times a week do
OR
account? you login to your Facebook
account? How long do you
stay logged in?
Invite students to brainstorm several other ideas for questions and continue the discussion.
ACTIVITY:
In pairs or teams…
1. Brainstorm (3-5 minutes)
Produce a list of about 4-6 survey questions that are of interest to your team.
Question Criteria: Survey population is the class/period for this activity, but could
eventually extend to a larger sample of students. Make your questions relevant,
interesting to student’s lives.
2. Select a question that you want to survey your class about.
3. On a large poster size sheet of paper, write the survey question, draw a chart, carefully label the
axes, and pair/team names.
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Time Spent Exercising per Week Minutes 46 − 60 > 75 < 30
30 − 45
61− 75 Represents an individual student sstudent 4. Post each survey question and graph on the walls around the room for a gallery walk.
5. In groups, students rotate around the room to each question, respond to the question by placing a
dot sticker in the appropriate place on the charts.
6. Pairs/teams return to their survey poster and discuss their data. (Students reproduce a chart using
the data they collected from class. This chart should probably begin as a bar graph, but other
types of graphs are acceptable if appropriate in representing data. Have students justify their
reasoning as to why they chose a particular type of graph to display their data.)
Some questions to stimulate discussion might include, “What did you notice about the data?”
“Did anything surprise you about your classmates’ responses?”
7. Whole class debrief, using the questions outlined in step #6.
DIRECT INSTRUCTION (Day 2):
Before you examine and analyze the data from the students’ surveys and histograms, introduce the
following terminology.
Students take notes Center of the data is determined by the median and the mean. The median is obtained by
ordering the values in a data set numerically, then finding the middle value or by finding the
average of two middle values. The mean is obtained by dividing the sum of the values by the
quantity of values in the data set.
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The shape of the data can be described as either symmetric, skewed to left, or
skewed to the right.
Symmetric – balanced, even
distribution of data to either side
of the center.
Skewed to the right (toward
larger values) appears to have
a larger number of responses
lie to the right of the peak of
the data.
Skewed to the left (toward
smaller values) appears to have a
larger number of responses that
lie to the left of the peak of data.
Activity Debrief: Begin debriefing the findings of each team’s survey by moving around the room to each poster
and facilitating the discussion. Below are some questions that can be asked of students during
the analysis.
• What is the median of the data set? (Students will estimate the median, calculate the
actual median, and compare results.) • What is the mean of the data set? (Students will estimate mean, calculate the actual
mean, and compare results.) • Describe the shape of the data set. Is it symmetrical? Skewed to the left? Or skewed to
the right? What is the significance of the shape? What does the data imply? • How does the shape of the data relate to the median and mean of the data set? • What conclusions can we draw from this data? Page 5 of 9
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Assessment: How many students were surveyed? __________
What is the actual mean of the data set?
__________
What is the actual median of the data set?
__________
minutes Describe the shape of the data set?
_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________
What conclusions can you draw from the chart data?
_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________
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Sample Responses: How many students were surveyed?
25 students were surveyed.
What is the actual mean of the data set?
The mean of the data set is 48 minutes.
What is the actual median of the data set?
The median of the data set is 45 minutes.
Describe the shape of the data set?
The data is fairly symmetric, but skewed slightly to the right, confirmed by the mean being
slightly larger than the median of the data set.
What conclusions can you draw from the chart data?
Sample Response: Most students spend between 30-60 minutes on homework each night.
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Warm-Up
5.MD.2
6.RP.5
One rainy week, Ruben placed a bucket
outside and measured the amount of rainfall
it collected each day. Below is the data he
recorded.
The table above shows the amount of money
raised during a fundraiser.
Sun
M
Tu
W
Th
F
Sat
6 in
5 in
8 in
7 in
6 in
9 in
1 in
Find the mean of the data set.
Who raised the least money?
Find the median of the data set.
Who raised the most money?
6.RP.3c
Which of the following is equal to
A) 4%
6.EE.7
4
?
25
Maria had 3 kilograms of sand for a science
experiment. She had to measure out exactly
1.625 kilograms for a sample. How much
sand will be left after she measures out the
sample?
B) 16%
C)
8
50
D) 0.08
E) 0.16
Check your solution using a different
method.
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Warm-Up: Answer Key
5.MD.2 6.RP.5 One rainy week, Ruben placed a bucket outside
and measured the amount of rainfall it
collected each day. Below is the data he
recorded.
Sun
M
Tu
W
Th
F
Sat
6 in
5 in
8 in
7 in
6 in
9 in
1 in
The table above shows the amount of money
raised during a fundraiser.
Find the mean of the data set.
[6 inches]
Who raised the least money? [Anne]
Find the median of the data set.
Who raised the most money? [Mike]
[6 inches]
6.RP.3c Which of the following is equal to
F)
4%
6.EE.7 4
?
25
Maria had 3 kilograms of sand for a science
experiment. She had to measure out exactly
1.625 kilograms for a sample. How much sand
will be left after she measures out the sample?
3 −1.625 = 1.375
G) 16% - KEY
H)
8
50 - KEY
Check your solution using a different method.
I) 0.08
-­‐1 -­‐0.625 J) 0.16 - KEY
0 1.375 2 3 Page 9 of 9
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