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The University of Texas at Austin
Department of Civil Engineering
CE 311S – Probability and Statistics for Civil Engineers
Handout No. 1
DATA REDUCTION
Many sources of uncertainty are inherent in civil engineering analysis and design.
A necessary
first step in any engineering situation is to investigate all available data and, then, to attempt to
assess the nature and the degree of the uncertainty relevant to the problem at hand.
We will see how graphical displays and numerical summaries of observed data can be used to
facilitate interpretation and evaluation.
For a single variable
Graphical Displays
A.
Histogram
1.
Sort the data in increasing order
2.
Note the range and divide it into an appropriate number,
k
, of intervals
Sturge’s Rule: Given
n
data, choose an integer closest to
k
for the number of intervals of
the histogram, where
k
= 1 + 3.32 log
10
(
n
).
Note that this is only a suggested value for the number of intervals.
You may use any
number of intervals but if you use too few or too many intervals, you may not get a good
graphical understanding of how the data are distributed.
It is also useful to try and make the interval sizes nice whole numbers (e.g., 4 in. rainfall
intensity bins in the example below) or multiples of 5, 10, 100, etc. depending on how
large in magnitude the data might be.
This might help adjust the value of
k
as well.
3.
Count the number of observations in each interval
4.
Plot the number of occurrences in each interval on a bar chart.
B.
Frequency Distribution
1.
Obtain the frequency of occurrences in each interval (the number of occurrences in the
interval divided by the total number of occurrences)
2.
Plot the frequency of occurrences in each interval on a bar chart.
C.
Frequency Density Distribution
1.
Divide the frequency of occurrences by the interval length
2.
Plot the frequency density in each interval on a bar chart (
note the units
).
What is the total area of all the bars in this diagram?
D.
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 Spring '08
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