Boxplots
Using the calculator to find mean, median,
standard deviation, quartiles….
O Put the data in L1
O Press STAT – Calc –
O #1 One Var Stat
Use the calculator to find mean, median,
standard deviation and interquartile range.
The following data represents the sodium content of
chocolate pudding made from instant mix:
3099
3112
2401
2824
2682
In 1997 a woman sued a computer keyboard manufacturer,
charging that her repetitive stress injuries were caused by the
keyboard. The jury awarded about $3.5 million for pain and
suffering, but the court then set aside that award and being
unreasonable compensation. In making this determination, the
court identified a “normative” group of 15 similar cases and
specified a reasonable award as within 2 standard deviations of
the mean of the awards in the 15 cases. What is the maximum
amount that could be awarded under the “2-standard deviations
rule? The following are the amount award in thousand of
dollars.
37
238
1050
75
340
1139
135
600
1200
140
750
1200
150
750
1576
Gross Product 2001
(in billions of dollars)
110
31
62
82
142
129
319
160
40
24
426
163
105
34
32
48
646
158
134
174
20
364
54
165
707
60
18
62
85
52
30
419
239
236
16
1119
77
63
100
254
295
17
231
142
107
41
21
40
161
341
193
O What percent are within one deviation of the
mean?
O What percent are within two deviations of the
mean?
Transforming Data
Transforming Data
O Transforming converts the original
observations from the original units of
measurements to another scale.
O Transformations can affect the shape,
center, and spread of a distribution.
What effect does adding have
on the data?
Effect of Adding (or
Subtracting) a Constant
O Adding the same number a (either positive,
zeros, or negative) to each observation
O Adds a to measures of center &
position(mean, median, percentiles, but
O Does not change the shape of the
distribution or measures of spread (range,
IQR, standard deviation).
What if I multiplied everything by
10?
Original Data
1
2
3
4
5
Effect of Multiplying (or
Dividing) by a Constant)
O Multiplying (or dividing) each observation by
the same number b (positive, negative, or
zero).
O Multiplies measures of center and location (mean,
median, quartiles, percentiles) by b
O Multiplies measures of spread (range, IQR, Standard
deviation) by |b|, but
O Does not change the shape of the distribution.
Original data has a mean of 50
and standard deviation of 5….
O What happens to both if we add 20 to each item?
O What happen to both is we multiply 20 to each item?
O What if we add 10 and multiply by 2?
Boxplots
O Provides information about the center,
spread, and symmetry (skewness) of the
data.
O Multiple boxplots can be used to compare
data.
Constructing a boxplot.
O Find the five number salary
O Minimum
O Q1
O Median
O Q3
O Maximum
O Plot on number line.
O Box in the IQR and draw whiskers to the min & max.
5, 8, 13, 17, 22, 24, 25, 27, 29, 30
8, 10, 22, 24, 25, 25, 26, 27, 45, 72
O Graph & Describe
Outlier
O A value is considered an outlier if it is more
than 1.5 IQR away from the closest end of
the box.
O It it is more than 3 IQR away from the
closest end of the box then it is called an
extreme outlier.
5, 7, 9, 9, 10, 11, 13, 17, 29
O Find if there are any outliers.
Using the Calculator.
O Put data in List
O Press 2nd stat
O Turn plot 1 on and choose boxplot
O Zoom 9
22, 27, 33, 39, 57, 88, 110
Modified Boxplot
O Mild outliers are represented by shaded
circles.
O Extreme outliers are represented by open
circles
O Whiskers are only extended to largest values
that are not outliers.
Create a Modified Boxplot
56
54
75
64
76
22
81
78
66
87
62
80
68
72
59
45
Comparative
O Measure your longest finger.
O Create boxplot of girls vs boys.
O Describe
Homework
O Worksheet