1. . . Box and Whisker Measures of Variation Measures of Variation 8 1216 20 24 28 32 36 40 44 48 52 56 60

2. Median 3, 4, 4, 5, 6, 7, 8 3, 4, 4, 5, 6, 7, 8, 9 Odd Number of Data
The middle number in a data set when the data are ordered from least to greatest.
Odd Number of Data
3, 4, 4, 5, 6, 7, 8
Even Number of Data
3, 4, 4, 5, 6, 7, 8, 9
5 + 6 = 11
= 5.5

3. Measures of Variation
Measures of variation are used to describe the distribution of the data.
median
20, , , , , , ,
Lower quartile
median
Upper quartile
= 44
= 52
= 61
= 26 61
2 = 22
2 = 30.5 44
Upper and Lower Quartiles
The upper and lower quartiles are the medians of the upper half and lower half of a set of data, respectively.
Lower quartile = 22
Upper quartile = 30.5
Interquartile Range
The range of the middle half of the data. It is the difference between the upper quartile and the lower quartile.
30.5 – 22 = 8.5
Range
The difference between the greatest and least data values
35 – 20 = 15

4. Measures of Variation
4, 4, 6, 7, 8, , , ,
Lower quartile
median
Upper quartile 5 8
13.5
Interquartile range
8.5
Range
19 - 4 15

5. Measures of Variation
4, 4, 6, 7, 8, , ,
Lower quartile
median
Upper quartile 5
7.5 11
Interquartile range 6
Range 15

6. Outlier
An outlier is a data value that is either much greater or much less than the median. If a data value is more than 1.5 times the value of the interquartile range beyond the quartiles, is an outlier.
2, , , , , , ,
Upper quartile
Lower quartile 22 26
Interquartile range 4
Outlier Test
Outlier Test
22 – 6 = 16
= 32
If 2 is less than
or equal to 16.
It is an outlier
If 31 is greater than
or equal to 32.
It is an outlier.
4 X 1.5 6
Subtract 6
Add 6
Pass
Fail

7. 9 4, 4, 6, 7, 8, 10, 12, 19 5 11 6 Outlier Test 7.5 Lower quartile
4, 4, 6, 7, 8, , ,
Lower quartile
median
Upper quartile 5
7.5 11
Interquartile range 6
5 – 9 = -4
= 20
Outlier Test
Outlier Test
6 X 1.5 9

8. 9 -7, 3, 5, 6, 8, 9, 11, 25 4 10 6 Outlier Test 7 Lower quartile
-7, 3, 5, 6, 8, 9, ,
Lower quartile
median
Upper quartile 4 7 10
Interquartile range 6
4 – 9 = -5
= 19
Outlier Test
Outlier Test
6 X 1.5 9

9. 12 -3, 4, 6, 7, 8, 9, 17, 24 5 13 8 Outlier Test 7.5 Lower quartile
-3, 4, 6, 7, 8, 9, ,
Lower quartile
median
Upper quartile 5
7.5 13
Interquartile range 8
5 – 12 = -7
= 25
Outlier Test
Outlier Test
8 X 1.5 12

10. 21 -3, -2, 4, 5, 5, 12, 18, 30 1 15 14 Outlier Test 5 Lower quartile
-3, , 4, 5, 5, , ,
Lower quartile
median
Upper quartile 1 5 15
Interquartile range 14
1 – 21 = -20
= 36
Outlier Test
Outlier Test
14 X 1.5 21

11. Box-and-Whisker Plots
A box-and-whisker plot is a diagram that is constructed using the median, quartiles, and extreme values. A box is drawn around the quartile values, and the whiskers extend from each quartile to the extreme values. The median is marked with a vertical line.
The outlier will be
shown with a small
symbol that is off the
Box-and-Whisker Plot . . . 8 12 16 20 24 28 32 36 40 44 48 52 56 60
median
Lower extreme
Upper extreme
Lower quartile
Upper quartile
Interquartile range
42 – 30 = 12

12. Box-and-Whisker Plots
8, , , , , , , , ,
Lower quartile
Upper quartile
median . . 26 . 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Outlier
Lower extreme
median
Upper extreme
Outlier
Lower quartile
Upper quartile
Interquartile range
= 9

13. Box-and-Whisker Plots
8, , , , , , , , , ,
Lower quartile
Upper quartile
median . . . 8 12 16 20 24 28 32 36 40 44 48 52 56 60
median
Upper extreme
Lower extreme
Lower quartile
Upper quartile
Interquartile range
= 12

14. Box-and-Whisker Plots
6, , , , , , , , , ,
Lower quartile
Upper quartile
median . . . 8 12 16 20 24 28 32 36 40 44 48 52 56 60
median
Lower extreme
Upper extreme
Lower quartile
Upper quartile
Outlier
Interquartile range
= 12

15. Box-and-Whisker Plots
12, , , , , , , , , ,
Lower quartile
Upper quartile
median . . . 8 12 16 20 24 28 32 36 40 44 48 52 56 60
median
Lower extreme
Upper extreme
Lower quartile
Upper quartile

16. Box-and-Whisker Plots
8, 9, , , , , , , , ,
Lower quartile
Upper quartile
median . . . 8 12 16 20 24 28 32 36 40 44 48 52 56 60
median
Lower quartile
Upper quartile
Lower extreme
Upper extreme

17. Box-and-Whisker Plots
16, , , , , , , , , ,
Lower quartile
Upper quartile
median . . . 8 12 16 20 24 28 32 36 40 44 48 52 56 60

18. Box-and-Whisker Plots. . . 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Median_______________
Upper quartile_________
Lower quartile_________
Upper extreme________
Lower extreme________
Outlier_______________ 30 40 24 50 16
no outlier

19. Box-and-Whisker Plots. . . 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Median_______________
Upper quartile_________
Lower quartile_________
Upper extreme________
Lower extreme________
Outlier_______________ 42 50 32 60 26 8

20. Box-and-Whisker Plots. . . 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Median_______________
Upper quartile_________
Lower quartile_________
Upper extreme________
Lower extreme________
Outlier_______________ 36 44 32 52 28 10

21. Box-and-Whisker Plots. . . 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Median_______________
Upper quartile_________
Lower quartile_________
Upper extreme________
Lower extreme________
Outlier_______________ 18 26 13 32 8 60