1. Chapter 6.4 Box and Whisker Plots

2. Quartile: include 𝑄 1 , 𝑄 2 , 𝑎𝑛𝑑 𝑄 3 Inter-quartile: 𝑄 3 - 𝑄 1

3. How to look at a Box Plot The least and greatest values show the range
The width of the box shows how consistent the data is.
A wide box shows very inconsistent data
A narrow box show a very consistent data
The location of the median shows the distribution of the data
Towards the middle means even distribution
Towards the side shows uneven distribution

4. Steps Order the data from least to greatest Find the median ( 𝑄 2 )
Find 𝑄 1 by finding the median of the lower half of the data (the left of the median)
Find 𝑄 3 by finding the median of the upper half of the data (the right of the median)
Find min value and max value

5. Inter-Quartile Range = 9 - 5½ = 3½
Finding the median, quartiles and inter-quartile range.
Example 1: Find the median and quartiles for the data below.
12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 10
Order the data
Lower Quartile = 5½ Q1
Median = 8 Q2
Upper Quartile = 9 Q3
4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12
Inter-Quartile Range = 9 - 5½ = 3½

6. Inter-Quartile Range = 10 - 4 = 6
Finding the median, quartiles and inter-quartile range.
Example 2: Find the median and quartiles for the data below.
6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10
Order the data
Lower Quartile = 4 Q1
Median = 8 Q2
Upper Quartile = 10 Q3
3, 4, 4, 6, 8, 8, 8, 9, , 10, 15,
Inter-Quartile Range = = 6

7. Discuss the calculations below.
2, 5, 6, 6, 7, 8, 8, 8, 9, 9, 10, 15
Median = 8 hours and the inter-quartile range = 9 – 6 = 3 hours.
Battery Life: The life of 12 batteries recorded in hours is:
Mean = 93/12 = 7.75 hours and the range = 15 – 2 = 13 hours.
Discuss the calculations below.
The averages are similar but the measures of spread are significantly different since the extreme values of 2 and 15 are not included in the inter-quartile range.

8. Boys Girls Box Plots Box and Whisker Diagrams. 4 5 6 7 8 9 10 11 12
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Boys
Girls cm
Box and Whisker Diagrams.
Box plots are useful for comparing two or more sets of data like that shown below for heights of boys and girls in a class.
Anatomy of a Box and Whisker Diagram.
Lowest Value
Upper Quartile
Highest Value
Median
Whisker
Box 4 5 6 7 8 9 10 11 12
Box Plots

9. Drawing a Box Plot. Boys Girls
2. The boys are taller on average.
Question: Gemma recorded the heights in cm of girls in the same class and constructed a box plot from the data. The box plots for both boys and girls are shown below. Use the box plots to choose some correct statements comparing heights of boys and girls in the class. Justify your answers.
Drawing a Box Plot.
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Boys
Girls cm
1. The girls are taller on average.
3. The girls show less variability in height.
4. The boys show less variability in height.
5. The smallest person is a girl.
6. The tallest person is a boy.

10. Finding the median, quartiles and inter-quartile range.
worksheet
Finding the median, quartiles and inter-quartile range.
12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 10
Example 1: Find the median and quartiles for the data below.
6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10
Example 2: Find the median and quartiles for the data below.
Worksheet 1

11. Exploration Go to my website: thanhthuycao.weebly.com
Go to Integrated Classwork April 10 and click on the website
Learn how to create box-and-whisker. Take good notes
Do QUESTIONSPROBLEMSCHALLENGE