Interquartile Range as a Measure of Variation

1
Interquartile Range as a Measure of Variation
Lesson 5
2
Warm Up
OBJECTIVE SWBAT distinguish between measures
of center and measures of variation and use
interquartile range (IQR) as a measure of
variation to describe data distributions. Language
Objective SWBAT write what measures of
variation are, how we find them, and why we use
them.
Yesterday in class, you filled out an index card
with real world examples of data sets with wide
ranges and narrow ranges. Today as our warm up,
the class will be tested on its understanding of
range using the examples you created!
Agenda
3
Warm Up
OBJECTIVE SWBAT distinguish between measures
of center and measures of variation and use
interquartile range (IQR) as a measure of
variation to describe data distributions. Language
Objective SWBAT write what measures of
variation are, how we find them, and why we use
them.

• After an example has been read aloud
• IN YOUR HEAD, determine whether the example
  represents a data set with a wide range or a
  narrow range.
• When you hear a clap, move your arms to represent
  your answer.

Arm Movements
Wide range Arms are outstretched Narrow range
Hands are close together
Agenda
4
Launch Review Turn and Talk (30 sec)
number of toppings students like
When we analyze data, what are we looking for?
Center
Spread (Measure of Variation)
Shape
Agenda
5
Launch Think-Pair-Share
Test Scores Would you expect a wide or narrow
range?
Twenty students take a social studies test. The
range of the scores is 98 points. The teacher
is worried that there is such a wide range of
scores. How do you think the students
performed?
Agenda
6
Launch Whole Class
The test scores are below.
7 68 70 70 72 76 80 80 80 82
84 85 85 87 88 90 90 92 93 105
How do you think the students performed?
Agenda
7
Launch Whole Class
In this example, was the range a useful measure
of variation to use to determine how a class of
students performed?
NO!!
Agenda
8
Explore Turn and Talk
Since the range is greatly influenced by
outliers, we also use the interquartile range
(IQR) to describe the variability of a data set.
Are there any parts of the word interquartile
that look familiar to you?
inter quartile
Agenda
9
Explore Notes
Quartiles the points that divide a data set into
roughly four equally-sized parts To divide
the data set into fourths 1) Find the
median
64
60
62
59
67
59
62
70
66
70
62
62
65
67
80
Agenda
9
9
10
Explore Whole Class
Now that we have found the median (64), how many
equal parts do we have?
Two roughly equal parts!
What should we do next to break our data set into
quartiles?
Break the two parts we have in half to make four
parts!
Remember that quartiles are the points that
divide a data set into roughly four equally-sized
parts!
59
59
60
62
62
62
62
64
65
66
67
67
70
70
80
Agenda
10
10
11
Explore Notes

• Quartiles the points that divide a data set into
  roughly four equally-sized parts
• To divide the data set into fourths
• Find the median
• Find the lower quartile (Q1) the median of all
  values below the median

59
59
60
62
62
62
62
64
65
66
67
67
70
70
80
Agenda
11
11
12
Explore Notes

• Quartiles the points that divide a data set into
  roughly four equally-sized parts
• To divide the data set into fourths
• Find the median
• Find the lower quartile (Q1) the median of all
  values below the median
• Find the upper quartile (Q3) the median of all
  values above the median

59
59
60
62
62
62
62
64
65
66
67
67
70
70
80
Agenda
12
12
13
Explore Check Your Work!
59
59
60
62
62
62
62
64
65
66
67
67
70
70
80
Agenda
13
14
Explore Independent
1. Quartiles divide a data set into roughly four
equally-sized parts. How could this be
illustrated in the figure below?
2. What percentage could we write above each
circle to show that each circle represents about
¼ of the data?
59
59
60
62
62
62
62
64
65
66
67
67
70
70
80
Hint
Agenda
Answer 1
Answer 2
15
Explore Independent
1. Quartiles divide a data set into roughly four
equally-sized parts. How could this be
illustrated in the figure below?
2. What percentage could we write above each
circle to show that each circle represents about
¼ of the data?
25 25 25 25
59
59
60
62
62
62
62
64
65
66
67
67
70
70
80
Q1 Q2 Q3 Q4
Next
16
Explore Turn-and-talk
Now that the data has been divided into four
groups, form statements about the set of data
below.
Word Bank 25 data Between ¼
25 25 25 25
59
59
60
62
62
62
62
64
65
66
67
67
70
70
80
Q1 Q2 Q3 Q4
25 of the days were between 59 and 62
1/4 of the days were between 67 and 80
Hint
Agenda
17
Explore Turn-and-talk
Now that the data has been divided into four
groups, form statements about the set of data
below.
Word Bank 25 data Between ¼
Possible sentence starters include 25 of the
days were between A quarter of the days
were below
25 25 25 25
59
59
60
62
62
62
62
64
65
66
67
67
70
70
80
Q1 Q2 Q3 Q4
25 of the days were between 59 and 62
1/4 of the days were between 67 and 80
Hint
Agenda
18
Explore Whole Class
Could we also form statements about the data
below using 50 or ½?
Word Bank Greater than 50 Between data Less
than ½
59
59
60
62
62
62
62
64
65
66
67
67
70
70
80
50 of the days were less than 64
Half of the days were between 62 and 67
Sentence Starters
Agenda
Hint
19
Explore Whole Class
Could we also form statements about the data
below using 50 or ½?
Word Bank Greater than 50 Between data Less
than ½
Possible sentence starters include 50 of the
days were between Half of the days were
above
59
59
60
62
62
62
62
64
65
66
67
67
70
70
80
50 of the days were less than 64
Half of the days were between 62 and 67
Sentence Starters
Agenda
Hint
20
Explore Whole Class
Could we also form statements about the data
below using 50 or ½?
Word Bank Greater than 50 Between data Less
than ½
59
59
60
62
62
62
62
64
65
66
67
67
70
70
80
50 of the days were less than 64
Half of the days were between 62 and 67
Sentence Starters
Agenda
Hint
21
Explore Turn and Talk
Now that we know what quartiles are, what is the
interquartile range?
Hint
Agenda
22
Explore Turn and Talk
Now that we know what quartiles are, what is the
interquartile range?
inter quartile
Hint
Agenda
23
Explore Vocabulary
What is the interquartile range? The
interquartile range is the difference between the
upper and lower quartiles in a data
set. Interquartile Range upper quartile (Q3)
lower quartile (Q1)
67 62 5
Agenda
24
Summary Think-Pair-Share
How could you explain the interquartile range in
sixth grade language?
Sentence starters could include The
interquartile range represents The
interquartile range is the spread of
Agenda
Scaffolding
25
Summary Think-Pair-Share
How could you explain the interquartile range in
sixth grade language?
Sentence starters could include The
interquartile range represents The
interquartile range is the spread of
Agenda
Scaffolding
26
Practice Part 1 Small Group
Lets go back to the test scores with a range of
98.
7 68 70 70 72 76 80 80 80 82
84 85 85 87 88 90 90 92 93 105
What is the interquartile range of the data?
Agenda
27
Practice Part 1 Whole Class
1) Find the median
7 68 70 70 72 76 80 80 80 82
84 85 85 87 88 90 90 92 93 105
Median 83 points
Agenda
28
Practice Part 1 Whole Class

1. Find the median
2. Find the lower quartile (Q1) the median of all
   values below the median

7 68 70 70 72 76 80 80 80 82
84 85 85 87 88 90 90 92 93 105
Agenda
29
Practice Part 1 Whole Class

1. Find the median
2. Find the lower quartile (Q1) the median of all
   values below the median
3. Find the upper quartile (Q3) the median of all
   values above the median

7 68 70 70 72 76 80 80 80 82
84 85 85 87 88 90 90 92 93 105
Agenda
30
Practice Part 1 Whole Class
Interquartile Range
89 74 15 points
Lower quartile (Q1) 74 points
7 68 70 70 72 76 80 80 80 82
84 85 85 87 88 90 90 92 93 105
Upper quartile (Q3) 89 points
Agenda
31
Practice Part 1 Think-Pair-Share

• Interquartile Range 89 74 15 points

What does an interquartile range of 15 points
actually mean?
7 68 70 70 72 76 80 80 80 82
84 85 85 87 88 90 90 92 93 105
Agenda
32
Practice Part 2
Part 2 - (10 Min) Work independently and check
in with a partner to complete your class work.
1-Worksheet
2-Share Out
Click on the timer!
In 10 minutes you will be asked to stop and share
your answers!
Agenda
33
Practice Student Share Out
Part 3 (5 Min) Students share
out work.
Classwork Questions
Agenda