Stage 4
Year 9
Interquartile
Range
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1
InterQuartile
Interquartile Range (1/7)
(The Range of the middle 50% of scores)
IQR = Q3 – Q1
What are Q3 and Q1?
Q1 is the lower quartile of 25th percentile.
Q3 is the upper quartile of 75th percentile.
Example 1
End of
1, 3, 5, 6, 7, 8, 8
Slide
Q1 = 3
Q3 = 8
IQR = Q3 - Q1
Middle of
Middle of
=8-3
lower half.
top half.
=5
Median = 6
2
Interquartile Range (2/7)
Median = 6
Q3 = 7
Middle of
top half.
Example 2
2, 3, 6, 6, 7, 8.
Q1 = 3
IQR = Q3 - Q1
=7-3
Middle of
=4
lower half.
Example 3
Median = 6.5
2, 3, 5, 6, 7, 9, 9, 10.
Q1 = 4
Q3 = 9
IQR = Q3 - Q1
=9-4
Middle of
Middle of
=5
lower half.
top half.
End of
Slide
3
Interquartile Range and Dot Plots (3/7)
Median
Q3
Q1
0
1
2
3
4
5
6
7
8
IQR = Q3 – Q1
=5–2
=3
End of
Slide
4
Interquartile Range and Stem-and-Leaf (4/7)
Stem
0
1
2
3
4
5
Leaf
0 1 2
1 3 3
4 4 5
2 3 4
5 7 7
0 5
6 Q1
5 6 Median
IQR = Q3 – Q1
7 7 9 9
= 38 – 13
6 8
Q3
9
= 25
End of
Slide
5
Interquartile Range - Box-and-Whisker (5/7)
B
E
C
D
A
A – Upper Extreme
B – Lower Extreme
C – Median
D – Upper Quartile – Q3
E – Lower Quartile – Q1
End of
Slide
6
Interquartile Range - Box-and-Whisker (6/7)
Q3
Q1
0
2
4
6
8 10 12 14 16
IQR = Q3 – Q1
= 13 – 3
= 10
End of
Slide
7
IQR – 5 Number Summary (7/7)
Lower
Extreme
0
Q1
2
Median
4
6
Q3
Upper
Extreme
8 10 12 14 16
Lower Extreme, Lower Quartile, Median, Upper Quartile, Upper Extreme
1, 3, 8, 13, 16
End of
Slide
8