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Lecture 2

ENVS178 Lecture Notes - Lecture 2: Summary Statistics, Negative Number, Watt


Department
Environmental Studies
Course Code
ENVS178
Professor
Jeff Casello
Lecture
2

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DISPLAYING DATA
De Veaux et al., Chapters 3 and 4
As a starting point, it makes sense to list, summarize or chart data before
doing any calculations. A visual inspection can help you to choose the
most appropriate techniques.
To illustrate some of the most common techniques for displaying
distributions, I will use the following data set of 30 observations of daily
maximum temperature (degrees C.).
Day
1
26.1 Day
11
25.9 Day
21
25.1
Day
2
25.3 Day
12
30.3 Day
22
22.0
Day
3
19.0 Day
13
32.3 Day
23
17.1
Day
4
18.0 Day
14
33.4 Day
24
11.1
Day
5
18.4 Day
15
34.0 Day
25
10.4
Day
6
18.4 Day
16
25.9 Day
26
10.3
Day
7
18.9 Day
17
17.3 Day
27
11.9
Day
8
25.8 Day
18
17.5 Day
28
11.6
Day
9
24.6 Day
19
16.9 Day
29
12.2

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Day
10
25.4 Day
20
24.9 Day
30
17.8
You should be asking questions about how the data were collected, for
example:
What type of instrument was used to measure maximum temperature?
How were these data recorded? a data logger? a human
technician?
How are the days defined? calendar days? morning to morning?
When and where were these data collected?
Are these sample data or do they include all the days for the relevant
study period?
Viewing the Data as a Time Series (line chart created in Excel)
Why use this graph:
See the change between two days
It is take away message; it will be on test.
It is important to keep the scale the same if u want to compare the results (ie. axis)
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930
0
5
10
15
20
25
30
35
40
Temperature Through Time
Day
Tem perature (degrees C)

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Frequency Distributions
Listing the Data as an Ordered Array: I have re-ordered the
observations in ascending order.
1234567891
01
11
21
31
41
51
6
10
.3
10
.4
11
.1
11
.6
11
.9
12
.2
16
.9
17
.1
17
.3
17
.5
17
.8
18
.0
18
.4
18
.4
18
.9
19
.0
1
71
81
92
02
12
22
32
42
52
62
72
82
93
0
22
.0
24
.6
24
.9
25
.1
25
.3
25
.4
25
.8
25
.9
25
.9
26
.1
30
.3
32
.3
33
.4
34
.0
Stem and Leaf Displays (or Stemplots) give an overall impression of
the frequency distribution, i.e. the frequency with which different values
occur.
Stems: »
Leaves: »
Stems and leaves are depends
It is common to truncate rather than round leaves. This produces a less
accurate display but it is much quicker and, since the intent of the stem
and leaf display is to get a visual impression, this practice is acceptable.
Stem and leaf displays of the temperature data:
Stem (whole
degrees)
Leaves (tenths of degrees)
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