Box-and-Whisker Plots

1. Box-and-Whisker Plots • We have learned various ways of organizing data so far. • We have learned • Line graphs • Bar Graphs • Tables • Next we will learn Box-and-Whisker Plots.

2. Box-and-Whisker Plots • Vocabulary • Box-and-Whisker Plot • Upper Quartile (UQ) • Lower Quartile (LQ) • Median • Upper Extreme • Lower Extreme • Interquartile range

3. Box-and-Whisker Plots • So what is a box and whisker plot? • A visual way to see the biggest number, lowest number, median of the set, median of the upper half of a set, and the median of the lower half of a set. • We will use a Box and lines extending from the box (whiskers) to show these values.

4. Box-and-Whisker Plots • To make a box-and-whisker plot, I need 5 things. (Before finding these, always put the data in order first.) • Upper Extreme (UE) • Lower extreme (LE) • Median • Upper Quartile (UQ) • Lower Quartile (LQ)

5. Five Values needed to make a Box-and-Whisker Plot 1. Upper Extreme- the largest value in a set of data. 2. Lower Extreme – the smallest value in a set of data. Ex. In the set 1,2,3,4,5,6,7; what is the upper extreme and the lower extreme? Upper Extreme: 7 Lower Extreme: 1

6. Five Values needed to make a Box-and-Whisker Plot 3. Median – Middle number when the values are written from least to greatest. 4. Upper Quartile (UQ) – When the values of a set are split into two groups by the median, the median of the upper half is called the upper quartile.

7. Example of Median • The median of this set of numbers is the number in the middle when the numbers are written in order. 1,2,3,4,5,6,7 • So what is the median of: 1,2,3,4,5,6,7 • So 4 is the median for our data set.

8. Example of Upper Quartile • Ex. Set of data: 1,2,3,4,5,6,7 • The numbers are written from least to greatest. The middle value is 4, so 4 is the median. • So 4 splits the numbers in half. • So now I cover up the median and look at all values to the RIGHT (the upper half). • 1,2,3,4,5,6,7 • The median of the values to the right of the median is called the upper quartile (UQ). • So what is the median of 5,6,7? 6 • So 6 is the upper quartile (UQ) for our data set.

9. Five Values needed to make a Box-and-Whisker Plot 5. Lower Quartile (LQ)- When the values of a set are split into two groups by the median, the median of the lower half is called the lower quartile.

10. Example of Lower Quartile (LQ) • Ex. Set of data: 1,2,3,4,5,6,7 • The numbers are written from least to greatest. The middle value is 4, so 4 is the median. • So 4 splits the numbers in half. • So now I cover up the median and look at all values to the LEFT (the lower half). • 1,2,3,4,5,6,7 • The median of the values to the right of the median is called the upper quartile (UQ). • So what is the median of 1,2,3? 2 • So 2 is the Lower Quartile (LQ) for our data set.

11. Five Values needed to make a Box-and-Whisker Plot • So now we have all five necessary items for our data set: 1,2,3,4,5,6,7 • Upper Extreme = 7 • Lower extreme = 1 • Median = 4 • Upper Quartile (UQ) = 6 • Lower Quartile (LQ) = 2

12. Box-and-Whisker Plot 4 1 2 6 7

13. Interquartile Range • Interquartile Range – subtract the lower quartile (left side of the box) from the upper quartile (right side of the box). • [UQ (right side of box )] – [LQ (left side of the box )] Example for our data UQ = 6 LQ = 2 Interquartile range = UQ – LQ = 6 – 2 = 4

14. 13 16 2 5 9 Box-and-Whisker Plot (Practice #1) 2, 4, 6, 8, 10, 12, 14, 16 UQ = LQ = UE = LE = Median = Create the box-and-whisker plot on your sheet.

15. 46 50 12 38 Box-and-Whisker Plot (Practice #2) 12, 15, 24, 31, 38, 39, 42, 50, 50 UQ = LQ = UE = LE = Median = 19.5 Create the box-and-whisker plot on your sheet.