1. NOTES # 5 GOALS: 1. STUDENTS LEARN HOW TO MAKE A BOX AND WHISKERS PLOT (BOX PLOT) 2.STUDENTS LEARN HOW TO USE THE IQR TO DETERMINE OUTLIERS. 3.STUDENTS WILL LEARN TO FIND WHAT IS THE PERCENTILE OF AN ITEM IN A DATA SET AS WELL AS WHICH ITEM IN A SET CORRESPONDS TO A CERTAIN PERCENTILE.

2. I. BOX AND WHISKERS PLOT Step1: Write the data set in increasing order Step2: Find the 5 number summary: Min, max, median (Q2), Q1 and Q3. Step3: Draw a number line. Plot the 5 pts. Make the box from Q1 to Q3. Draw the Whiskers one from min to Q1 and the second from Q3 to max.

3. EXAMPLE: -7, 6, 1, 2, 8, 0, 2, 2, 3, Order: -7, 0, 1, 2, 2, 2, 3, 6, 8 min= ____ median(Q2) = _____ max = ____ Q1= ______ Q3= _____ 2 0.54.5 8 -7 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

4. You try this one: Draw a box plot. 3, 4, 7, 6, 8, 8, 7, 18, 11, 10, 8, 1, 1

5. II. Interquartile Range (IQR) Checking for Outliers Any Number < Q1 – 1.5xIQR Would be an outlier on the left Any Number > Q3+1.5xIQR Would be an outlier on the Right IQR =Q3-Q1

6. Ex: -7, 0, 1, 2, 2, 2, 3, 6, 8 Q1 = 0.5 and Q3= 4.5 IQR = 4.5-0.5=4 Any Number < Q1 – 1.5xIQR Would be an outlier on the left. so Any Number < 0.5 – 1.5x4 Any Number < 0.5 – 6 Any number smaller than -5.5 Thus -7 is an Outlier on the left Any Number > Q3+1.5xIQR Would be an outlier on the right. so Any Number > 4.5 + 1.5x4 Any Number > 4.5 + 6 Any number bigger than 10.5 Thus there are no Outliers on the right

7. You try this one: Find outliers. 3, 4, 7, 6, 8, 8, 7, 18, 11, 10, 8, 1, 1

8. less than or equal The pth percentile of a set of numbers is a value in the set such that p percent of the numbers are less than or equal to the value.

9. Max always at the 100 th percentile Often but not always: Median is at 50 th percentile Q1 is at the 25 th percentile Q3 is at the 75 th percentile Minimum depends on the number of numbers

10. Ex 1: 17, 2, 6, 5, 13, 8, 1, 15 (Make sure they are in ORDER) a)What is the percentile for 15? b)What # corresponds with the 63 rd percentile? Ex 1: 1, 2, 5, 6, 8, 13, 15, 17

11. Ex 2: 105, 8, 5, 96, 9, 13, 28, 9, 100, 103, 211 (Make sure they are in ORDER) a)What is the percentile for 96? b)What # corresponds with the 22 nd percentile? Ex 2: 5, 8, 9, 9, 13, 28, 96, 100, 103, 105, 211