1. Trenton Public Schools
Box and Whisker Graph
Slide Presentation By
Mr. Michael Braverman
Trenton Public Schools
March 2015

2. Box and Whisker Graph Why? To compare similar sets of data
quickly and easily, even if they
have different numbers of elements.

3. Box and Whisker Graph Set C 2 5 1 9 6 6
Start with a new piece of graph paper.
Draw a box and whisker graph for set C.

4. order from lowest to highest.
Box and Whisker Graph
Set C
Step 1: Start by ranking the data in
order from lowest to highest.
Set C

5. Step 2: Find the midway point (median)
Box and Whisker Graph
Step 2: Find the midway point (median)
Set C
Median is halfway between 5 and 6.

6. Step 3: Find the quartiles
Set C
median
The median of the lower half is the lower quartile
The median of the upper half is the upper quartile

7. Step 4: Find the ’mums
Set C LQ UQ
median
minimum
maximum

8. Step 5: Organize your data!
Set C
median LQ UQ
minimum
maximum
min 1 LQ 2
med
5.5 UQ 6
max 9

9. Step 6: Graph your data Set C 1 2 5 6 6 9 min 1 LQ 2 med 5.5 UQ 6 max
1. Draw a number line that goes from the min to the max (it may go past them!)
Set C

10. Step 6: Graph your data Set C 1 2 5 6 6 9 min 1 LQ 2 med 5.5 UQ 6 max
2. Draw a vertical line above the number line for each piece of data.
Set C

11. Step 6: Graph your data Set C 1 2 5 6 6 9 min 1 LQ 2 med 5.5 UQ 6 max
3. Connect the middle three lines at the top and bottom to form a box.
Set C

12. Step 6: Graph your data Set C 1 2 5 6 6 9 min 1 LQ 2 med 5.5 UQ 6 max
4. Connect the maximum and minimum to the box in the center to form the whiskers
Set C
Note 1: The box will ALWAYS be between the maximum and minimum, but it will not necessarily be in the center of it!

13. Step 6: Graph your data Set C 1 2 5 6 6 9 min 1 LQ 2 med 5.5 UQ 6 max
4. Connect the maximum and minimum to the box in the center to form the whiskers
Set C
Note 2: The quartiles separate the data roughly into quarters.

14. Step 7: “See” the fourths
min 1 LQ 2
med
5.5 UQ 6
max 9
Set C 1 4 1 4 1 4 1 4
Note 2: The quartiles separate the data roughly into quarters. ¼ of 6 = 1.5, so there should be one or two pieces of data per section.

15. Graph Multiple sets of data over the same number line to compare!

16. Practice
Create a box and whisker graph for each of the followiing sets: D: E:

17. Solution D: 2 4 7 8 9 19 Min LQ Med UQ Max E: 10 12 13 14 15 7.5 11
14.5 D: E:

18. Solution D: 2 4 7 8 9 19 Min LQ Med UQ Max E: 10 12 13 14 15 D E min 211
med
7.5 13 UQ 9
14.5
max 19 15
7.5 D:
Min LQ Med UQ Max E: 11
14.5 D: E:

19. Solution E D 0 2 4 6 8 10 12 14 16 18 20 D E min 2 10 LQ 4 11 med 7.513 UQ 9
14.5
max 19 15 D: E: E D

20. More: E D
Suppose this is a graph of home runs hit by two different players.
Why would someone argue that D was a better home run hitter?
Why would someone argue that E was a better home run hitter?
Who would you pick for your team? Why? What other questions would you need to answer before you make that decision?

21. Outliers
1. Data far enough away from the rest of the data to distort the “average”
2. Data more than 1.5 times the Interquartile range above the upper quartile or below the lower quartile.

22. Outliers
Data more than 1.5 times the Interquartile range above the upper quartile or below the lower quartile.
Interquartile Range = the distance between the Upper
Quartile and Lower Quartile
IQR = UQ - LQ
IQR = 9 - 4
= 5
IQR D

23. Outliers D IQR = 5 1.5 * IQR = 1.5 * 5 = 7.5
Data more than 1.5 times the Interquartile range above the upper quartile or below the lower quartile.
IQR = * IQR = 1.5 * 5 = 7.5 = =
IQR
IQR
IQR D
The UPPER BORDER for outliers is 16.5.
The LOWER BORDER for outliers is -3.5

24. Outliers D
The UPPER BORDER for outliers is 16.5.
The LOWER BORDER for outliers is -3.5
Data more than 1.5 times the Interquartile range above the upper quartile or below the lower quartile.
Therefore, any data above 16.5 is an outlier. Note that since
The maximum is higher than 16.5, we have at least one
outlier. There are no outliers at the lower end because the
minimum is higher than the LOWER BORDER