Stat 101: 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 in weight is the weight of
the contents. The units are grams.
1
Weight 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
Stat 101: 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
Stat 101: 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
Stem and Leaf
34
35
36
37
9
12334455567
25678899
0038
8
Weight of Contents
W eight of C ontents of C ans of C ola
Frequency
15
10
5
0
33 0
340
35 0
36 0
370
38 0
390
W eight (gram s)
9
Stat 101: Lecture 4
Shape
• Symmetry
–Mounded, flat
• Skew
–Right, left
• Other
–Multiple peaks, outliers
10
Symmetric
Mounded in the 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
11
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
12
Stat 101: Lecture 4
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
13
Multiple Peaks
Size of Diamonds (carats)
Frequency
15
10
5
0
0.1
0.2
0.3
0.4
Size (carats)
14
Weight of Contents
W eight of Contents of Cans of Cola
Frequency
10
5
0
330
340
350
360
370
380
390
W eight (grams)
15