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

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 Q1, the median, and the third quartile Q3.

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.

1. Turn calculator on2. 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 Enter2. Number should now be in L13. Continue until all numbers are entered for L1

1. After all data for 1 set/list is entered for L1, click STAT

2. Arrow to the right to CALC3. Click Enter for 1-Var Stats4. New screen should have 1-Var Stats at

top1. Click 2nd (blue key)2. Click L1 (the #1 key)3. Click Enter4. You should now have a list of statistics

Used to construct a boxplot Consists of the Minimum value, Q1,

median (or Q2), Q3, 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

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 Q1 = 45 Median (med) = 90 Q3 = 97.5 Maximum value (maxX) = 100

You will need your 5 Number Summary data Determine the IQR (Interquartile Range)

Q3 – Q1

To calculate outliers on the left side (low side) Multiply 1.5 x the IQR Subtract Q1 from that number

To calculate outliers on the right side (high number side) Multiply 1.5 x the IQR Add that number to Q3

Example: IQR = Q3 – Q1 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 Q1 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

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.

1. To create a boxplot on the TI – 83/84 Calculator:

2. Enter numbers in L1 as directed above3. After data is entered do the following:

1. (If 5 number summary screen is showing, click CLEAR, STAT, Enter on EDIT)

2. Press 2nd3. Click Y= (at very top, gray button), you

should have STAT PLOTS at top4. Click Enter for Plot 1 to be ON

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 ENTER4. Xlist should have L1 for the list you are

using; if not, change it here5. Click ZOOM (at top, gray button)6. Click the number 97. Voila! You should have a boxplot

Minimum value (minX) = 0Q1 = 45Median (med) = 90Q3 = 97.5Maximum value (maxX) = 100

0 25 50 75 100 125

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)

1. To create a modified boxplot on the TI – 83/84 Calculator:

2. Enter numbers in L1 as directed above3. After data is entered do the following:

1. (If 5 number summary screen is showing, click CLEAR, STAT, Enter on EDIT)

2. Press 2nd3. Click Y= (at very top, gray button), you

should have STAT PLOTS at top4. Click Enter for Plot 1 to be ON

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 ENTER4. Xlist should have L1 for the list you are

using; if not, change it here5. Mark: choose the outlier mark you would like6. Click ZOOM (at top, gray button)7. Click the number 98. Voila! You should have a modified boxplot

showing outliers, if any

Minimum value (minX) = 0Q1 = 45Median (med) = 90Q3 = 97.5Maximum value (maxX) = 100Outliers below 33.75 (1 at point 0)Outliers above 176.25 (none)

0 25 50 75 100 125