Measure of Position: Percentile

1. Measure of Position: Percentile

2. A measure of position describes_____________________________________________ __________________________________________________________________. Percentiles are a measure of position that_______________________________________ __________________________________________________________________. For example, _____ of the data values are equal to or below the _____ percentile. the location of one value in relation to the others in the distribution indicate the percentage of values below or equal to the given value. 30% 30th

3. We can use the formula below to calculate the percentile of a value in a distribution: *If the answer is not an integer round up to the nearest integer*

4. Example 1: Here is a distribution containing 50 values. • 6, 7, 8, ..., 19, 21, 21, 21, 23, 24, ..., 50, 51, 52, 52, 55, 59 • a) Find the percentile of 21. 20 values 15 values Percentile of 21 = = The percentile is 51 so 51% of values are below or equal to 21 = 0.51 * 100 = 51

5. Example 1: Here is a distribution containing 50 values. 6, 7, 8, ..., 19, 21, 21, 21, 23, 24, ..., 50, 51, 52, 52, 55, 59 b) Find the percentile of 50 20 values 15 values Percentile of 50 = = = 0.88 * 100 = 88

6. We can also use the following equation to find the position or total number of data values less than or equal to the value: *If the answer is not an integer, round it down to an integer*

7. Example 2: Using the same values from Example 1, 6, 7, 8, ..., 19, 21, 21, 21, 23, 24, ..., 50, 51, 52, 52, 55, 59 a) Find the position of the 75th percentile 20 values 15 values The 75th percentile is in the 37th spot =37.5 *Round down to 37* =37

8. Example 2: Using the same values from Example 1, 6, 7, 8, ..., 19, 21, 21, 21, 23, 24, ..., 50, 51, 52, 52, 55, 59 b) Find the position of the 65th percentile. 20 values 15 values =32.5 *Round down to 32* =32

9. Homework: Percentile Homework sheet