1. CCM1A – Dr. Fowler Unit 2 – Lesson 3 Box-and-Whisker Plots

2. Video - Box and Whisker Plot – Basketball Application

3. Measures of Spread How much do values typically vary from the center?
Range
Interquartile Range (IQR)
Standard Deviation
Today’s focus will be on standard deviation.

4. Example 1 – You are given a set of numbers
Step 1 - Order the set of numbers from least to greatest (very important)

5. Step 2 – Find the Median
2. Find the median. The median is the middle number. If the data has two middle numbers, find the mean of the two numbers. What is the median?

6. Step 3 – Upper & Lower Quartiles
3. Find the lower and upper medians or quartiles. These are the middle numbers on each side of the median. What are they?

7. Step 4 – Draw a Number Line
Now you are ready to construct the actual box & whisker graph. First you will need to draw an ordinary number line that extends far enough in both directions to include all the numbers in your data:

8. Step 5 – Draw the Parts
Locate the main median 12 using a vertical line just above your number line:

9. Step 5 – Draw the Parts
Locate the lower median 8.5 and the upper median 14 with similar vertical lines:

10. Step 5 – Draw the Parts
Next, draw a box using the lower and upper median lines as endpoints:

11. Step 5 – Draw the Parts
Finally, the whiskers extend out to the data's smallest number 5 and largest number 20:

12. Step 6 - Label the Parts of a Box-and-Whisker Plot
Lower Quartile
Upper Quartile
Median 3 1 2
Upper Extreme
Lower Extreme 4 5
Name the parts of a Box-and-Whisker Plot

13. 14 – 8.5 = 5.5 Interquartile Range
The interquartile range is the difference between the upper quartile and the lower quartile.
14 – 8.5 =
5.5

14. Try One: Draw a Box & Whisker Plot
3, 5, 4, 2, 1, 6, 8, 11, 14, 13, 6, 9, 10, 7

15. Order numbers
3, 5, 4, 2, 1, 6, 8, 11, 14, 13, 6, 9, 10, 7
First, order your numbers from least to greatest:
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14

16. Median
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14
Then find the median (from the ordered list):
Cross off one number from each side until you reach the middle number (or numbers).
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14

17. Median (continued):
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14
If there are two numbers in the middle,
Add those 2 middle numbers together:
6 + 7 = 13
Then divide by 2:
13 ÷ 2 = 6.5
The median is 6.5.

18. Quartiles (page 1)
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14
Then split the numbers on left and right sides of the median:
1, 2, 3, 4, 5, 6, 6, │7, 8, 9, 10, 11, 13, 14

19. Quartiles (page 2)
1, 2, 3, 4, 5, 6, 6, │7, 8, 9, 10, 11, 13, 14
Find the median for each half:
1, 2, 3, 4, 5, 6, 6 │ 7, 8, 9, 10, 11, 13, 14
1, 2, 3, 4, 5, 6, 6 │ 7, 8, 9, 10, 11, 13, 14
Left Right
Median = Median = 10

20. Quartiles (page 3)
1, 2, 3, 4, 5, 6, 6 │ 7, 8, 9, 10, 11, 13, 14
Left Right
Median = Median = 10
The left median is called the LOWER QUARTILE.
The right median is called the UPPER QUARTILE.

21. Number line
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14
Draw a number line from the smallest to the largest number without skipping any numbers.

22. Quartiles on number line
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14
Put circles at the LOWER and UPPER Quartiles.

23. Box on Quartiles on number line
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14
Draw a box connecting the circles at the LOWER and UPPER Quartiles.

24. Median on number line
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14
Put a circle at the median (6.5).

25. Median on number line
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14
Draw a line connecting the median to the box.

26. Low and high numbers
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14
Put circles at the high and low points.

27. Low and high numbers
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14
Draw lines that connect the high and low points to the box.

28. Box and Whisker Plot
3, 5, 4, 2, 1, 6, 8, 11, 14, 13, 6, 9, 10, 7
Here is the completed Box and Whisker Plot!