1. Percentiles For any whole number P (between 1 and 99), the Pth percentile of a distribution is a value such that P% of the data fall at or below it. The percent falling above the Pth percentile will be (100 – P)%.

2. Percentiles 40% of data Lowest value Highest value P 40 60% of data

3. Quartiles Percentiles that divide the data into fourths Q 1 = 25th percentile Q 2 = the median Q 3 = 75th percentile

4. Quartiles Q1Q1 Median = Q 2 Q3Q3 Inter-quartile range = IQR = Q 3 — Q 1 Lowest value Highest value

5. Computing Quartiles Order the data from smallest to largest. Find the median, the second quartile. Find the median of the data falling below Q 2. This is the first quartile. Find the median of the data falling above Q 2. This is the third quartile.

6. Find the quartiles: 12 15 16 16 17 18 22 22 23 24 25 30 32 33 33 34 41 45 51 The data has been ordered. The median is 24.

7. Find the quartiles: 12 15 16 16 17 18 22 22 23 24 25 30 32 33 33 34 41 45 51 The data has been ordered. The median is 24.

8. Find the quartiles: 12 15 16 16 17 18 22 22 23 24 25 30 32 33 33 34 41 45 51 For the data below the median, the median is 17. 17 is the first quartile.

9. Find the quartiles: 12 15 16 16 17 18 22 22 23 24 25 30 32 33 33 34 41 45 51 For the data above the median, the median is 33. 33 is the third quartile.

10. Find the interquartile range: 12 15 16 16 17 18 22 22 23 24 25 30 32 33 33 34 41 45 51 IQR = Q 3 – Q 1 = 33 – 17 = 16

11. Five-Number Summary of Data Lowest value First quartile Median Third quartile Highest value

12. Box-and-Whisker Plot a graphical presentation of the five-number summary of data

13. Making a Box-and-Whisker Plot Draw a vertical scale including the lowest and highest values. To the right of the scale, draw a box from Q 1 to Q 3. Draw a solid line through the box at the median. Draw lines (whiskers) from Q 1 to the lowest and from Q 3 to the highest values.

14. Construct a Box-and-Whisker Plot: 12 15 16 16 17 18 22 22 23 24 25 30 32 33 33 34 41 45 51 Lowest = 12Q 1 = 17 median = 24Q3 = 33 Highest = 51

15. Box-and-Whisker Plot Lowest = 12 Q 1 = 17 median = 24 Q3 = 33 Highest = 51 60 - 55 - 50 - 45 - 40 - 35 - 30 - 25 - 20 - 15 - 10 -