1. Box-and-Whisker Plots

2. What is a box and whisker plot? A box and whisker plot is a visual representation of how data is spread out and how much variation there is. It doesn’t show all the data values, but instead focuses on the median, extremes, and quartiles. Video

4. Median The median is the middle value of an ordered set of numbers. -Example: 2 3 7 11 14 -In this case the median is 7. Note: If there is an even amount of data values, the median is found by adding the 2 middle values together and then dividing that number by 2. -Example: 2 3 7 11 14 19 -In this example: 7 + 11 = 18. Then 18/2 = 9. The median is 9.

5. Extremes The extremes are the highest and lowest values of the data set. -Example: 2 3 7 11 14 -In this case, the lower extreme is 2 and the upper extreme is 14.

6. Quartiles The quartiles are the median of the higher half of the data set and the median of the lower half of the data set. -Example: 2 3 7 11 14 -Since the median was 7, we don’t include that number when finding the quartiles. -The lower quartile is 2.5 -The upper quartile is 12.5

7. Quartiles The quartiles are the median of the higher half of the data set and the median of the lower half of the data set. -Example: 2 3 7 11 14 19 -Since the median was 9 we need to include 7 when finding the lower quartile and include 11 when finding the upper quartile. -The lower quartile is 3 -The upper quartile is 14

8. How to read a box-and-whisker plot. Dots outside of the box and whiskers are outliers. Maximum and minimum values are shown at the ends of each whisker. The upper and lower quartiles are the ends of the box. The median is the line in the middle of the box. The max, min, LQ, UQ, and Median make up the “Five Number Summary”. Outlier Min Lower quartile Median Upper quartile Max Outlier

9. Let’s do an Example Together… Here are the temperatures for each day in August. August 69 70 71 71 72 72 72 73 74 75 75 76 76 76 77 77 77 77 77 78 78 80 81 82 82 83 83 85 85 90 93 Min Max Median LQ UQ

10. What does the graph tell you? The lowest temperature: 69 degrees Fahrenheit The highest temperature: 93 degrees Fahrenheit. Range: 93-69 = 24 The Median: 77 degrees Fahrenheit. The Lower Quartile: 73 degrees Fahrenheit. The Upper Quartile: 82 degrees Fahrenheit. The Interquartile Range: 82-73 = 9 Since the medians (3 of them) represent the middle points, they split the data into 4 equal parts. – 25% of the data numbers are less than 73 – 25% of the data numbers are between 73 and 77 – 25% of the data numbers are between 77 and 82 – 25% of the data numbers are greater than 82

11. Example 1 Ruby asked the students in her class how long their families spent making dinner each night. This box-and-whisker plot shows the results. Find the following values: Minimum:LQ: Maximum:UQ: Range:Interquartile Range:Median: 20 25 5045 30 20 35

12. You Try! A professor asked her students to keep track of how many websites they visit each day. This box-and-whisker plot shows the results. Find the following values: Minimum:LQ: Maximum:UQ: Range:Interquartile Range:Median: 4510 8 6 3 7

13. Practice: Box and Whisker Plots Worksheet