1. 11.2B Box- and Whisker Plots Statistics Mrs. Spitz Fall 2008

2. Objectives To get a more complete picture of the data. Be able to figure out the first quartile, third quartile, and interquartile range.

3. Assignment 11.2B

4. Introduction The purpose of calculating a mean or median is to obtain one number that describes some measurements. That one number alone; however, may not adequately represent the data.

5. Definitions A box-and-whisker plot is a graph that gives a more complete picture of the data. It shows five numbers: 1.The smallest value 2.The first quartile 3.The median, 4.The third quartile and 5.The greatest value

6. First/Third Quartile definitions Symbolized by Q 1, the number below which one-quarter of the data lie. The third quartile, symbolized by Q 3 is the number above which one-quarter of the data lie.

7. Example Find the first quartile Q 1 and the third quartile Q 3 for the prices of 15 half- gallon cartons of deluxe ice cream. 3.264.714.184.455.493.183.863.584.295.444.834.564.362.392.66 To find the quartiles, first arrange the data from the smallest value to the largest value. Then find the median.

8. Example Find the first quartile Q 1 and the third quartile Q 3 for the prices of 15 half- gallon cartons of deluxe ice cream. 3.264.714.184.455.493.183.863.584.295.444.834.564.362.392.66 To find the quartiles, first arrange the data from the smallest value to the largest value. Then find the median. 2.392.663.183.263.583.864.184.294.364.454.564.714.835.445.49 The median is 4.29.

9. Example Now separate the data into two groups. Those values below the median and those values above the median. 4.364.454.564.714.835.445.49 2.392.663.183.263.583.864.18 Values less than medianValues greater than median Q1Q1 Q3Q3 The first quartile Q 1 is the median of the lower half of the data: Q 1 = 3.26 The third quartile Q 3 is the median of the upper half of the data: Q 3 = 4.71

10. Interquartile Range Definition Is the difference between the third quartile Q 3 and the first quartile Q 1. Interquartile range = Q 3 – Q 1 = 4.72 – 3.26 = 1.45 Fifty percent of the data in a distribution lie in the interquartile range.

11. Box-and-Whisker Plots Shows the data in the interquartile range as a box. The box-and-whisker plot for the data on the cost of ice cream is shown below. 2.393.26 4.294.71 5.49 Q1Q1 Q3Q3 Median

12. Box-and-Whisker Plots Note that the box-and-whisker plot labels five values: the smallest (2.39); the first quartile Q 1 (3.26), the median (4.29); the third quartile Q 3, 4.71; and the largest value (5.49). 2.393.26 4.294.71 5.49 Q1Q1 Q3Q3 Recall from the last section that the difference between the largest and smallest values is called the RANGE. For these data: Range = 5.49 – 2.39 = 3.10 Median

13. Example For these next two examples, use the data in the following table. I am putting it vertically, so you can read it. 3045 5424 4838 4338 4653 6264 4035

14. Find the first quartile and third quartile for the data in the software training table. Strategy: Arrange the data from smallest to largest. Then find the median Find Q 1 as the median of the lower half of the data. Find Q 3 as the median of the upper half of the data. Draw a box and whiskers plot for the data in the software training table.

15. Example For these next two examples, use the data in the following table. I am putting it vertically, so you can read it. 3045 5424 4838 4338 4653 6264 4035 24303538 404345464853546264 Arrange data from least to greatest.

16. Find the median 24303538 404345464853546264 Oops, there are an even number, so you must take the two middle numbers, add them together and divide by 2. Median = 43 + 45 = 44 2

17. Next find the median of the top lower half and the upper half. 24303538 4043 Median = 53; so Q 3 = 53 Median =38; so Q 1 = 38 45464853546264

18. Draw the Line and plot points 2438 4453 64

19. Draw a box – neatly and label 1 st and 3 rd quartile and median 2438 4453 64 Q1Q1 Q3Q3 Median

20. Homework Answers 1.Mean = 19 Median = 19.5 9. 72 yds. 2.Mean = 381.56 Median =394.5 10. 21 3. Mean = 10.61 Median = 10.605 11. 77 4.Mean = 45.615 Median = 45.855 12. 2 5. Median13. German Chocolate cake 6. mean – 88.3 Median = 94 14. brown 7.Mean = 17.45 Median = 17 15. Satisfactory 8.Mean =403.63 Median =411 16. very good