Box and Whisker Plots

1. Box and Whisker Plots C. D. Toliver AP Statistics

2. Percentile • The percentile of a distribution of a set of data is a value such that p% of the data fall at or below the data value and (100-p%) of the data fall at or above it. • Example 1– suppose you scored 2000 on your SAT and your score report said you fell in the 89th percentile. Then 89% of the test takers scored a 2000 or less and 11% of the test takers scored 2000 or more • Example 2 – The top 15% of the graduating class at WOS has a GPA of 3.9 or higher. That means they are at least in the 85th percentile. 85 % of the students have a GPA of 3.9 or less.

3. Quartiles • Special percentiles (100% divided into fourths). So we consider data in the • 25th percentile, quartile 1 (Q1) • Median or 50th percentile, quartile 2 (Q2) • 75th percentile, quartile 3 (Q3)

4. How to Compute Quartiles • Order the data from smallest to largest. • Find the median. This is the second quartile, Q2. • The first quartile Q1 is the median of the lower half of the data; that is, it is the median of the data falling below Q2, but not including Q2 • The third quartile Q3 is the median of the upper half of the data; that is, it is the median of the data falling above Q2 but not including Q2

5. Example 1-Consider the data set:{10, 20, 30 40, 50, 60, 70} • The median, Q2 is 40 • Q1 is the median of the values below 40, These values are 10, 20, and 30. The median, or Q1 is 20. • Q3 is the median of the values above 40, These values are 50, 60 and 70 so the median or Q3 is 60.

6. Interquartile Range • The interquartile range is the difference between Q3 and Q1 or Q3 –Q1 For our data set Q1 is 20, Q3 is 60, so the interquartile range is 60-20 = 40

7. Five-Number Summary • Lowest Value or minimum • Q1 • Median • Q3 • Highest value or maximum

8. Five-Number Summary • Example - For the data set {10,20,30,40,50,60,70}: • The five number summary is • Lowest number, 10 • Q1, 20 • Median, 40 • Q3, 60 • Highest number, 70

9. Box and Whisker Plot • A box and whisker plot is a graphical display of the five number summary • Draw a scale to include the lowest and highest data values • Draw a box from Q1 to Q3 • Include a solid line through the box at the median • Draw solid lines, called whiskers from Q1 to the lowest value and from Q3 to the highest value.

10. TI 84 1-Variable Stats

11. TI 84 1-Variable Stats

12. TI 84 1-Variable Stats

13. TI 84 Box and Whisker Plot

14. TI 84 Box and Whisker Plot

15. TI 84 Box and Whisker Plot

16. TI 84 Box and Whisker Plot

17. TI 84 Box and Whisker Plot

18. TI 84 Box and Whisker Plot

20. Questions • Is the median always in the middle of the box of your box and whiskers plot? • How do outliers affect a box and whiskers plot? • How can you use a box and whiskers plot to tell if your data is skewed right or skewed left? • What would be a better way to display the data if you want to see the actual outliers?

21. Example 2 • Compute the five-number summary and draw a box and whiskers plot for the test scores on a recent AP Statistics test • {76, 59, 76, 78, 100,66,63,70,89,87,81,48,78} • What scores if any might be considered outliers? • How do they affect the shape of the graph? • How would the graph change if you removed the outliers?

23. Example 3 • Compute the five-number summary and draw a box and whiskers plot for the test scores on a recent AP Statistics test in another class. • {87,78,91,70,70,66,87,78,80,86,97,98,97,94} • What scores if any might be considered outliers? • How do they affect the shape of the graph? • How would the graph change if you removed the outliers? • Compare the two sets of data? What can you conclude about the test results for the two classes?