Transcript Boxplot - Sophia

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Boxplot
TI-83/84 Calculator
5 number summary
Do you have an outlier
Modified Boxplot
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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.
Turn calculator on
Press STAT (should see EDIT CALC TESTS
across the top)
Press Enter (for Edit)
You should now have a screen with L1, L2, L3,
etc.
For a set of numbers, enter in L1:
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Type the number and click Enter
Number should now be in L1
Continue until all numbers are entered for L1
After all data for 1 set/list is entered for L1,
click STAT
Arrow to the right to CALC
Click Enter for 1-Var Stats
New screen should have 1-Var Stats at top
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Click 2nd (blue key)
Click L1 (the #1 key)
Click Enter
You should now have a list of statistics
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Used to construct a boxplot
Consists of the Minimum value, Q1, median (or
Q2), Q3, and the maximum value
Example:
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Using the directions on the previous 2 slides enter
the following data: 90, 100, 90, 0, 95.
Identify the 5 number summary
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Example:
Using the directions on the previous 2 slides
enter the following data: 90, 100, 90, 0, 95.
Identify the 5 number summary
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Minimum value (minX) = 0
Q1 = 45
Median (med) = 90
Q3 = 97.5
Maximum value (maxX) = 100
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You will need your 5 Number Summary data
Determine the IQR (Interquartile Range)
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To calculate outliers on the left side (low side)
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Q3 – Q1
Multiply 1.5 x the IQR
Subtract Q1 from that number
To calculate outliers on the right side (high
number side)
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Multiply 1.5 x the IQR
Add that number to Q3
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Example:
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IQR = Q3 – Q1
IQR = 97.5 – 45 = 52.5
To calculate outliers on the left side (low side)
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1.5 x 52.5 = 78.75 (1.5 x IQR)
Subtract Q1 from that number
 78.75 – 45 = 33.75
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To calculate outliers on the right side (high
number side)
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1.5 x 52.5 = 78.75 (1.5 x IQR)
97.5 + 78.75 = 176.25
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Outliers on the left side (low side)
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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)
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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.
To create a boxplot on the TI – 83/84
Calculator:
Enter numbers in L1 as directed above
After data is entered do the following:
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(If 5 number summary screen is showing, click
CLEAR, STAT, Enter on EDIT)
Press 2nd
Click Y= (at very top, gray button), you should have
STAT PLOTS at top
Click Enter for Plot 1 to be ON
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You should now have a blinking cursor on
ON, click ENTER
Arrow down to Type and select (with arrows)
to the middle one in the second row
Click ENTER
Xlist should have L1 for the list you are using;
if not, change it here
Click ZOOM (at top, gray button)
Click the number 9
Voila! You should have a boxplot
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Minimum value (minX) = 0
Q1 = 45
Median (med) = 90
Q3 = 97.5
Maximum value (maxX) = 100
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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)
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To create a modified boxplot on the TI – 83/84
Calculator:
Enter numbers in L1 as directed above
After data is entered do the following:
1.
2.
3.
1.
2.
3.
4.
(If 5 number summary screen is showing, click
CLEAR, STAT, Enter on EDIT)
Press 2nd
Click Y= (at very top, gray button), you should have
STAT PLOTS at top
Click Enter for Plot 1 to be ON
1.
2.
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You should now have a blinking cursor on ON,
click ENTER
Arrow down to Type and select (with arrows) to
the first one in the second row
Click ENTER
Xlist should have L1 for the list you are using; if
not, change it here
Mark: choose the outlier mark you would like
Click ZOOM (at top, gray button)
Click the number 9
Voila! You should have a modified boxplot
showing outliers, if any
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25
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100
Minimum value (minX) = 0
Q1 = 45
Median (med) = 90
Q3 = 97.5
Maximum value (maxX) = 100
Outliers below 33.75 (1 at point 0)
Outliers above 176.25 (none)
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