Stat 101L: Lecture 4
Quantitative Data
For a Statistics’ project, students
weighed the contents of cans of
cola.
In 2000, 24 cans of cola were
weighed (full and empty). The
difference (full – empty) is the
weight of the contents. The units
are grams.
1
Quantitative Data
Who? Cans of cola.
What? Weight (g) of contents.
368, 351, 355, 367, 352, 369, 370, 369
370, 355, 354, 357, 366, 353, 373, 365
355, 356, 362, 354, 353, 378, 368, 349
2
Weight of Contents
What can we say about the weight
of contents of a can of cola?
– Variation!
– Smallest value?
– Largest value?
– Middle value?
3
1
Stat 101L: Lecture 4
Display of Data
Stem-and-Leaf Display
or Stem Plot
– Orders the data and creates a
display of the distribution of
values.
4
Display of Data
Histogram
– A picture of the distribution of the
data.
– Collects values into bins.
– Bins should be of equal width.
– Different bin choices can yield
different pictures.
5
Frequency
Histogram
Measurement
6
2
Stat 101L: Lecture 4
Constructing a
Histogram
Order data from smallest to
largest using a stem and leaf
display.
Determine bins.
– equal width
– more data
more bins
7
Weight of Contents
W eight of Contents of Cans of Cola
Frequency
15
10
5
0
3 30
340
350
360
37 0
38 0
390
W eight (gram s )
8
Shape
Symmetry
– Mounded, flat
Skew
– Right, left
Other
– Multiple peaks, outliers
9
3
Stat 101L: Lecture 4
Symmetric, mounded in
middle
Histogram of Octane Rating
10
9
8
Frequency
7
6
5
4
3
2
1
0
86
87
88
89
90
91
92
93
94
95
96
Octane
10
Skew - Right
pH of Pork Loins
80
70
Frequency
60
50
40
30
20
10
0
5.0
5.5
6.0
6.5
7.0
pH
11
Skew - Left
Flexibility Index of Young Adult Men
20
Frequency
15
10
5
0
1
2
3
4
5
6
7
8
9
10
Flexibility Index
12
4
Stat 101L: Lecture 4
Multiple Peaks
Size of Diamonds (carats)
15
Frequency
10
5
0
0.1
0.2
0.3
0.4
Size (carats)
13
Center
A typical value.
Summary of the whole batch of
numbers.
For symmetric distributions –
easy.
14
Histogram of Octane
Histogram of Octane Rating
10
9
8
Frequency
7
6
5
4
3
2
1
0
86
87
88
89
90
91
92
Octane
93
94
95
96
Center
15
5
Stat 101L: Lecture 4
Spread
Variation matters.
– Tightly clustered?
– Spread out?
– Low and high values?
16
Numerical
Summaries
Weights of contents of cans of cola.
34 9
35 12334455567
36 25678899
37 0038
17
Numerical
Summaries
What is a “typical” value?
Look for the center of the
distribution.
What do we mean by
“center”?
18
6
Stat 101L: Lecture 4
Measures of Center
Sample Midrange
–Average of the minimum and
the maximum.
(349+378)/2=363.5 grams
–Greatly affected outliers.
19
Measures of Center
Sample Median
– A value that divides the data into a
lower half and an upper half.
– About half the data values are
greater than the median about half
are less than the median.
20
Sample Median
34 9
35 12334455567
36 25678899
37 0038
Median = (357+362)/2
= 359.5 grams
21
7