2.  Boxplot  TI-83/84 Calculator  5 number summary  Do you have an outlier  Modified Boxplot

3.  A boxplot is a graph of a data set that consists of a line extending from the minimum value to the maximum value and a box with lines drawn at the first quartile Q 1, the median, and the third quartile Q 3.  Also called a box and whisker diagram. The lines extending from the box are called whiskers.  The dark line in the box is the median.

4. 1. Turn calculator on 2. Press STAT (should see EDIT CALC TESTS across the top) 3. Press Enter (for Edit) 4. You should now have a screen with L1, L2, L3, etc. 5. For a set of numbers, enter in L1: 1. Type the number and click Enter 2. Number should now be in L1 3. Continue until all numbers are entered for L1

5. 1. After all data for 1 set/list is entered for L1, click STAT 2. Arrow to the right to CALC 3. Click Enter for 1-Var Stats 4. New screen should have 1-Var Stats at top 1. Click 2nd (blue key) 2. Click L1 (the #1 key) 3. Click Enter 4. You should now have a list of statistics

6.  Used to construct a boxplot  Consists of the Minimum value, Q 1, median (or Q 2 ), Q 3, and the maximum value  Example:  Using the directions on the previous 2 slides enter the following data: 90, 100, 90, 0, 95.  Identify the 5 number summary

7.  Example:  Using the directions on the previous 2 slides enter the following data: 90, 100, 90, 0, 95.  Identify the 5 number summary  Minimum value (minX) = 0  Q 1 = 45  Median (med) = 90  Q 3 = 97.5  Maximum value (maxX) = 100

8.  You will need your 5 Number Summary data  Determine the IQR (Interquartile Range)  Q 3 – Q 1  To calculate outliers on the left side (low side)  Multiply 1.5 x the IQR  Subtract Q 1 from that number  To calculate outliers on the right side (high number side)  Multiply 1.5 x the IQR  Add that number to Q 3

9.  Example:  IQR = Q 3 – Q 1  IQR = 97.5 – 45 = 52.5  To calculate outliers on the left side (low side)  1.5 x 52.5 = 78.75 (1.5 x IQR)  Subtract Q 1 from that number  78.75 – 45 = 33.75  To calculate outliers on the right side (high number side)  1.5 x 52.5 = 78.75 (1.5 x IQR)  97.5 + 78.75 = 176.25

10.  Outliers on the left side (low side)  If you have outliers to the left of the median (the left side, lower numbers), then it will be data that is less that 33.75, in this example, which is 0.  Outliers on the right side (high side)  If you have outliers to the right of the median (the right side, higher numbers), then it will be data that is greater than 176.25, in this example, which we have none.

11. 1. To create a boxplot on the TI – 83/84 Calculator: 2. Enter numbers in L1 as directed above 3. After data is entered do the following: 1. (If 5 number summary screen is showing, click CLEAR, STAT, Enter on EDIT) 2. Press 2nd 3. Click Y= (at very top, gray button), you should have STAT PLOTS at top 4. Click Enter for Plot 1 to be ON

12. 1. You should now have a blinking cursor on ON, click ENTER 2. Arrow down to Type and select (with arrows) to the middle one in the second row 3. Click ENTER 4. Xlist should have L1 for the list you are using; if not, change it here 5. Click ZOOM (at top, gray button) 6. Click the number 9 7. Voila! You should have a boxplot

13. Minimum value (minX) = 0 Q 1 = 45 Median (med) = 90 Q 3 = 97.5 Maximum value (maxX) = 100 0 255075100125

14.  Boxplot constructed with the following modifications:  Special symbol (usually an asterisk or dot) to identify outliers  Solid horizontal line (left whisker) extends only to the minimum data (minX)  Solid horizontal line (right whisker) extends only to the maximum data (maxX)

15. 1. To create a modified boxplot on the TI – 83/84 Calculator: 2. Enter numbers in L1 as directed above 3. After data is entered do the following: 1. (If 5 number summary screen is showing, click CLEAR, STAT, Enter on EDIT) 2. Press 2nd 3. Click Y= (at very top, gray button), you should have STAT PLOTS at top 4. Click Enter for Plot 1 to be ON

16. 1. You should now have a blinking cursor on ON, click ENTER 2. Arrow down to Type and select (with arrows) to the first one in the second row 3. Click ENTER 4. Xlist should have L1 for the list you are using; if not, change it here 5. Mark: choose the outlier mark you would like 6. Click ZOOM (at top, gray button) 7. Click the number 9 8. Voila! You should have a modified boxplot showing outliers, if any

17. Minimum value (minX) = 0 Q 1 = 45 Median (med) = 90 Q 3 = 97.5 Maximum value (maxX) = 100 Outliers below 33.75 (1 at point 0) Outliers above 176.25 (none) 0 255075100125