Lecture_E7_statistics

Lecture_E7_statistics - Lecture 18 Probability Statistics...

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Unformatted text preview: Lecture 18: Probability, Statistics, Interpolation • Histograms • Probability • ormal Distribution Normal Distribution • Random Number Generation • ummary Summary Reference: book, Chapter 7 Histogram •A histogram is a plot of frequency of occurrence of data values versus the values themselves. xample 1: A class of 20 students with 20 scores Example 1: A class of 20 students with 20 scores Test 1: 61, 61, 65, 67, 69, 72, 74, 74, 76, 77, 83, 83, 85, 88, 89, 92, 93, 93, 95, 98 Test 2: 66, 69, 72, 74, 75, 76, 77, 78, 78, 79, 79, 80, 81, 83, 84, 85, 87, 88, 90, 94 10 Histogram of Test2, mean value = 79.75 10 Histogram of Test1, mean value = 79.75 6 8 r of Scores 6 8 r of Scores 2 4 Number 2 4 Numbe 60 70 80 90 100 Score Range 60 70 80 90 100 Score Range Histogram Functions: hist, bar hist(y); [z,x] = hist(y): Aggregates the data in the vector y into 10 bins evenly spaced between the minimum and maximum values in y. Returns two vectors z and x that contain the frequency count and the bin locations. hist(y,n); [z,x] = hist(y,n): Aggregates the data in the vector y into n bins evenly spaced between the minimum and maximum values in y. Returns two vectors z and x that ontain the frequency count and the bin locations contain the frequency count and the bin locations. hist(y,x); [z,x] = hist(y,x): Aggregates the data in the vector y into bins whose center locations are specified by the vector x. The bin widths are the distances between the centers. Returns two vectors z and x that contain the frequency count and the bin locations. bar(x,y): Creats a bar chart of y versus x Example: Using hist(y) Analyze the Absolute Frequency and Relative Frequency of a data set using histogram. xample 2: Given measured temperature data (F) in 20 days: Example 2: Given measured temperature data (F) in 20 days: 90, 89, 80, 82, 83, 97, 92, 91, 100, 102, 84, 79, 85, 87, 94, 93, 99, 85, 86, 78. 4 Frequency Absolute Frequency Histogram 75 80 85 90 95 100 105 2 Temperature Absolute F y 2 4 te Frequency 75 80 85 90 95 100 105 Temperature Absolu Example: Absolute histogram using n bins Using 15 bins 4 ency Absolute Frequency Histogram using 15 bins 5 5 5 00 05 2 bsolute Freque 75 80 85 90 95 100 105 Temperature A 4 Frequency 75 80 85 90 95 100 105 2 Temperature Absolute F Example: Relative histogram using specific bins 6 uency Absolute Frequency Histogram using specified bins Absolute Frequency tal number of events Relative Frequency = 5 5 5 00 2 4 Absolute Freq...
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Lecture_E7_statistics - Lecture 18 Probability Statistics...

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