Transcript Box Plots and Outliers

Box Plots and Outliers
Box Plot
We need 5 numbers, called the 5 number
summary:
1. minimum value
2. Q1
3. median
4. Q3
5. maximum value
Harry Potter Data
The 5 number summary is:
Minimum
Q1
Median
Q3
Maximum
70.9
78.9
81.35
84.45
86.2
Drawing the plot free hand
• Use a scaled line to draw the box plot
• Approximate locations of the values.
• We say this is SKEWED LEFT since the
longer tail is on the left side.
Using the TI
• Put the data into the list
• Press y = ; make sure that there is nothing
in the 10 equations
• Press 2nd key, y =
• There are 3 statistical plots.
• Press #1
• Turn the plot ON
• Select the 2nd box plot
• Make the x list L1
• Press Zoom
• Press Enter on #9
• The Box plot will appear
• Press TRACE to see values; use right or
left arrow keys to move around.
Inter-quartile Range
• The inter-quartile range (IQR) is the value
of Q3 – Q1
Outliers
• An outlier is an unusual score, relative to
the data set. It will influence the mean and
the standard deviation.
• A data set might have no outliers, one
outlier, or several outliers.
• Two types: Mild and Extreme
Mild Outliers
Look for data values (x)
that are either:
1.
2.
Q3 + 1.5 IQR < x  Q3 + 3 IQR
Extreme Outliers
Look for values that are either:
1.
2.
Harry Potter data - checking
Example: Ages of actresses at the
time they first won the Oscar
50
44
35
80
26
28
41
21
61
38
49
33
74
30
33
41
31
35
41
42
37
26
34
34
35
26
61
60
34
24
30
37
31
27
39
34
26
25
33
5 number summary for actresses
•
•
•
•
•
Min = 21
Q1 = 30
Med = 34
Q3 = 41
Max = 80
Actresses
• Check for outliers. Identify type.
Box plot with outliers
• When we select the 1st box plot on the TI,
it allows us to see outliers. Select the
mark that is visible for you.
• Zoom #9 results in:
• Trace and go to the right twice.
• The 50 is the last data value that is not an
outlier.
Comparison of Boxplots and
histograms