1. Interquartile Range as a Measure of Variation

2. Launch – Review Turn and Talk (30 sec)
number of toppings students like
When we analyze data, what are we looking for?
Median
Center
Mean
Range
Today!
Spread
(Measure of Variation)
Interquartile Range
Mean Absolute Deviation
Shape

3. 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?

4. Launch Whole Class
The test scores are below. 7 68 70 72 76 80 82 84 85 87 88 90 92 93
105
How do you think the students performed?

5. 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!!

6. Explore Turn and Talk inter quartile
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
Between
Quarters

7. 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°
67°
59°
62°
59°
70°
66°
70°
62°
62°
67°
65°
80°
59°
60°
62°
64°
65°
66°
67°
70°
80°
median 7 7

8. 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°
median 8 8

9. 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°
lower quartile (Q1) 9 9

10. 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°
upper quartile (Q3) 10 10

11. Explore Check Your Work!
median
upper quartile (Q3)
lower quartile (Q1)
59°
59°
60°
62°
62°
62°
62°
64°
65°
66°
67°
67°
70°
70°
80° 11

12. 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°
Answer #1
Answer #2

13. 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% %
59°
59°
60°
62°
62°
62°
62°
64°
65°
66°
67°
67°
70°
70°
80°
Q Q2 Q Q4

14. 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% %
59°
59°
60°
62°
62°
62°
62°
64°
65°
66°
67°
67°
70°
70°
80°
Q Q2 Q Q4
“25% of the days were between 59° and 62°”
“1/4 of the days were between 67° and 80°”

15. Explore Turn-and-talk
Now that the data has been divided into four groups, form statements about the set of data below.
Possible sentence starters include:
“25% of the days were between…”
“A quarter of the days were below…”
Word Bank
25% data
Between ¼
25% % 25% %
59°
59°
60°
62°
62°
62°
62°
64°
65°
66°
67°
67°
70°
70°
80°
Q Q2 Q Q4
“25% of the days were between 59° and 62°”
“1/4 of the days were between 67° and 80°”

16. 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°”
Hint

17. 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°”
Hint

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
median
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°”
Hint

19. Explore Turn and Talk
Now that we know what quartiles are, what is the interquartile range?

20. Explore Turn and Talk
Now that we know what quartiles are, what is the interquartile range?
inter quartile
Between
Quarters

21. 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°
Interquartile range
59°
60°
62°
64°
65°
66°
67°
70°
80°
lower quartile (Q1)
upper quartile (Q3)

22. Practice – Part 1 Small Group
Let’s go back to the test scores with a range of 98. 7 68 70 72 76 80 82 84 85 87 88 90 92 93
105
What is the interquartile range of the data?

23. Practice – Part 1 Whole Class
1) Find the median 7 68 70 72 76 80 82 84 85 87 88 90 92 93
105
Median = 83 points

24. Practice – Part 1 Whole Class
Find the median
Find the lower quartile (Q1): the median of all values below the median
Lower quartile (Q1) = 74 points 7 68 70 72 76 80 82 84 85 87 88 90 92 93
105

25. Practice – Part 1 Whole Class
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 7 68 70 72 76 80 82 84 85 87 88 90 92 93
105
Upper quartile (Q3) = 89 points

26. Practice – Part 1 Whole Class
Interquartile Range =
89 – 74 = 15 points
Lower quartile (Q1) = 74 points 7 68 70 72 76 80 82 84 85 87 88 90 92 93
105
Upper quartile (Q3) = 89 points

27. Practice – Part 1 Think-Pair-Share
Interquartile Range = – 74 = 15 points
What does an interquartile range of 15 points actually mean? 7 68 70 72 76 80 82 84 85 87 88 90 92 93
105