Lesson 13-5

1. Lesson 13-5 Box-and-Whisker Plots

2. Transparency 5 Click the mouse button or press the Space Bar to display the answers.

3. Transparency 5a

4. Objectives • Organize and use data in box and whisker plots • Organize and use data in parallel box and whisker plots

5. Vocabulary • Box and whisker plot – • Extreme values –

6. Box-and-Whiskers Plot whiskers part • Parts of the Plot: • Smallest data value (not an outlier) • Largest data value (not an outlier) • Quartiles 1, 2 and 3 (Q1, Q2 also known as median, Q3) • Outliers – any data value that is outside the following range: [Q1 – 1.5IQR, Q3 + 1.5IQR] box part Q1 Q2 Q3 smallest* largest* * - not an outlier

7. Example 1a EcologyThe average water level in Lake Travis in central Texas during August is a good indicator of whether the region has had normal rainfall, or is suffering from a drought. The following is a list of the water level in feet above sea level during August for the years 1990 to 2000. 674, 673, 678, 673, 670, 677, 653, 679, 664, 672, 645 Draw a box-and-whisker plot for these data.

8. 645, 653, 664, 670, 672, 673, 673, 674, 677, 678, 679 Example 1a cont Step 1 Determine the quartiles and any outliers. Order the data from least to greatest. Use this list to determine the quartiles. Determine the interquartile range. Check to see if there are any outliers. Any numbers less than 644.5 or greater than 696.5 are outliers. There are none.

9. Example 1a cont Step 2 Draw a number line. Assign a scale to the number line that includes the extreme values. Above the number line, place bullets to represent the three quartile points, any outliers, the least number that is not an outlier, and the greatest number that is not an outlier. 664 673 645 679 677

10. Example 1a cont Step 3 Complete the box-and whisker plot. Draw a box to designate the data between the upper and lower quartiles. Draw a vertical line through the point representing the median. Draw a line from the lower quartile to the least value that is not an outlier. Draw a line from the upper quartile to the greatest value that is not an outlier.

11. Example 1b What does the box-and-whisker plot tell about the data? Notice that the whisker and the box for the top half of the data is shorter than the whisker and box for the lower half of the data. Answer: The upper half of the data are less spread out than the lower half of the data; data is skewed left.

12. Example 2 ClimatePilar, who grew up on the island of Hawaii, is going to go to college in either Dallas or Nashville. She does not want to live in a place that gets too cold in the winter, so she decided to compare the average monthly low temperatures of each city. Draw a parallel box-and-whisker plot for the data. Determine the quartiles and outliers for each city.

13. Dallas32.7, 36.3, 36.9, 45.4, 45.6, 54.7, 55.8, 62.6, 66.9, 70, 73.6, 74.1 Nashville26.5, 29.9, 30.9, 39.1, 39.6, 47.5, 48.3, 56.6, 61.1, 64.7, 67.7, 68.9 Example 2 cont Neither city has any outliers. Draw the box-and-whisker plots using the same number line.

14. Example 2 cont Answer: Use the parallel box-and-whisker plots to compare the data. Answer:The interquartile range of temperatures for both cities is about the same. However, all quartiles of the Dallas Temperatures are shifted to the right of those of Nashville, meaning Dallas has higher average low temperatures.

15. Summary & Homework • Summary: • The vertical rule in the box of a box-and-whisker plot represents the median • The box of a box-and-whisker plot represents the interquartile range • The bullets at each end of a box-and-whisker plot are the extremes • Parallel box-and-whisker plots can be used to compare data • Homework: • pg 740 10-26 even