Handout No. 1 - Data Reduction

Handout No. 1 - Data Reduction - The University of Texas at...

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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.

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