11.2B Box-and Whisker Plots

1. 11.2B Box-and Whisker Plots

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. 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.

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

5. First/Third Quartile definitions • Symbolized by Q1, the number below which one-quarter of the data lie. The third quartile, symbolized by Q3 is the number above which one-quarter of the data lie.

6. Example • Find the first quartile Q1 and the third quartile Q3 for the prices of 15 half-gallon cartons of deluxe ice cream. To find the quartiles, first arrange the data from the smallest value to the largest value. Then find the median.

7. Example • Find the first quartile Q1 and the third quartile Q3 for the prices of 15 half-gallon cartons of deluxe ice cream. To find the quartiles, first arrange the data from the smallest value to the largest value. Then find the median. The median is 4.29.

8. Example Now separate the data into two groups. Those values below the median and those values above the median. Values less than median Values greater than median Q3 Q1 The first quartile Q1 is the median of the lower half of the data: Q1 = 3.26 The third quartile Q3 is the median of the upper half of the data: Q3 = 4.71

9. Interquartile Range Definition • Is the difference between the third quartile Q3 and the first quartile Q1. Interquartile range = Q3 – Q1 = 4.71 – 3.26 = 1.45 Fifty percent of the data in a distribution lie in the interquartile range.

10. 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. Q1 Median Q3 5.49 2.39 3.26 4.29 4.71

11. Q1 Q3 5.49 2.39 3.26 4.29 4.71 Box-and-Whisker Plots • Note that the box-and-whisker plot labels five values: the smallest (2.39); the first quartile Q1 (3.26), the median (4.29); the third quartile Q3, 4.71; and the largest value (5.49). Median 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

12. Example • For these next two examples, use the data in the following table. I am putting it vertically, so you can read it.

13. 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 Q1 as the median of the lower half of the data. • Find Q3 as the median of the upper half of the data. • Draw a box and whiskers plot for the data in the software training table.

14. Example • For these next two examples, use the data in the following table. I am putting it vertically, so you can read it. Arrange data from least to greatest.

15. Find the median 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

16. Next find the median of the top lower half and the upper half. Median =38; so Q1 = 38 Median = 53; so Q3 = 53

17. Draw the Line and plot points 64 24 38 44 53

18. Draw a box – neatly and label 1st and 3rd quartile and median Median Q1 Q3 64 24 38 44 53