Box and Whisker Plots

1. Box and Whisker Plots

2. Box and Whisker Plot A box and whisker plot is a diagram or graph that shows quartiles and extreme values of a set of data.

3. Five Number Summary • Median • LQ (Lower Quartile) • UQ (Upper Quartile) • Minimum • Maximum

4. Let’s review how to find the Five Number Summary… Here are the number of gold medals won by the top 16 countries in the 1992 summer Olympics.

5. First, put the numbers in order from least to greatest. 3, 3, 4, 5, 6, 6, 7, 8, 11, 12, 13, 14, 16, 33, 37, 45 5.5 LQ 9.5 Med 15 UQ Min Max Second, find the median, lower quartile (LQ), and upper quartile (UQ). Third, find the minimum & maximum. Min = 3 LQ = 5.5 Med = 9.5 UQ = 15 Max = 45 This is called a “five number summary.”

6. Before we can make the box plot, we need to check for outliers. An outlier is a number that is 1.5 Interquartile Ranges (IQR) above the UQ and below the LQ. Okay, now I am lost!! IQR = UQ - LQ

7. Steps to Finding Outliers 1. IQR = UQ - LQ 2. IQR · 1.5 3. Add answer from #2 to UQ. 4. Subtract answer from #2 from LQ. Anything greater than your answer to #3 is an outlier. Anything less than your answer to #4 is also an outlier.

8. Before we can draw the box and whisker plot, we also need to find outliers. Outliers are numbers that are 1.5 IQR’s above or below LQ & UQ. Min = 3 LQ = 5.5 Med = 9.5 UQ = 15 Max = 45 14.25 + 15 = 29.25 5.5 - 14.25 = -8.75 IQR = UQ - LQ 15 - 5.5 = 9.5 So… the outliers are… x > 29.25 OR x < -8.75 9.5 ·1.5 = 14.25

9. 3, 3, 4, 5, 6, 6, 7, 8, 11, 12, 13, 14, 16, 33, 37, 45 5.5 LQ 9.5 Med 15 UQ Min Max 33, 37, and 45 are outliers for this data. Now we have all the information we need to draw the box and whisker plot.

10. To draw the box and whisker plot, you need the five number summary and the outliers. Min = 3 LQ = 5.5 Med = 9.5 UQ = 15 Max = 45 Outliers: 33, 37, 45 First, draw a number line that will accommodate the data range.

11. * * * 0 5 10 15 20 25 30 35 40 45 50 LQ, Med, and UQ form the box. The outliers are marked with asterisks. The “whiskers” connect the box with the last numbers that are not outliers. You have just drawn a box and whisker plot!

12. * * * 0 5 10 15 20 25 30 35 40 45 50 Box and whisker plots are divided into quartiles. Each quartile contains 1/4 or 25% of the data. Even though the quartiles do not appear to be equal, they all contain an equal amount of data. For this box and whisker plot... 1st fourth of data: x < 5.5 2nd fourth of data: 5.5 < x < 9.5 3rd fourth of data: 9.5 < x < 15 4th fourth of data: x > 15

13. * * * 0 5 10 15 20 25 30 35 40 45 50 Using the box and whisker plot: What percent of the teams won 6 and 15 gold medals? About 50% What does the plot tell us about the upper half of the data compared to the lower half? The upper half is more spread out while the lower half is closely clustered together.

14. Here is the time in which 10 students ran a mile: 10, 12, 8, 10, 9, 10, 9, 11, 10, 18 Find the “five number summary”, the outliers, and draw a box and whisker plot of the data. Click when you are ready for the answer.

15. 7 8 9 10 11 12 13 14 15 16 17 18 19 8, 9, 9, 10, 10, 10, 10, 11, 12, 18 Min LQ 10 Med UQ Max Five Number Summary: Min = 8 LQ = 9 Med = 10 UQ = 11 Max = 18 Outliers: x < 6 x > 14 So… 18 is an outlier. *

16. There are more examples of box and whisker plots in your book. Happy graphing!