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Probability and Statistics for Engineers

Learn about descriptive statistics, measures of central tendency, variability, probability distributions, and statistical inference for engineers. Understand numerical values that characterize data, calculation of mean and median, variability measures, and graphical representation methods.

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Probability and Statistics for Engineers

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  1. Probability and Statistics for Engineers • Descriptive Statistics • Measures of Central Tendency • Measures of Variability • Probability Distributions • Discrete • Continuous • Statistical Inference • Design of Experiments • Regression EGR 252 Spring 2013

  2. Descriptive Statistics • Numerical values that help to characterize the nature of data for the experimenter. • Example: The absolute error in the readings from a radar navigation system was measured with the following results: • the sample mean, x = ? 17 22 39 31 28 52 147 EGR 252 Spring 2013

  3. Calculation of Mean • Example: The absolute error in the readings from a radar navigation system was measured with the following results: _ • the sample mean, X = (17+ 22+ 39 + 31+ 28 + 52 + 147) / 7 = 48 17 22 39 31 28 52 147 EGR 252 Spring 2013

  4. Calculation of Median • Example: The absolute error in the readings from a radar navigation system was measured with the following results: • the sample median, x = ? • Arrange in increasing order: 17 22 28 31 39 52 147 • n odd median = x (n+1)/2 , → 31 • n even median = (xn/2 + xn/2+1)/2 • If n=8, median is the average of the 4th and 5th data values. 17 22 39 31 28 52 147 ~ EGR 252 Spring 2013

  5. Descriptive Statistics: Variability • A measure of variability • Example: The absolute error in the readings from a radar navigation system was measured with the following results: • sample range = Max – Min = 147 – 17 = 130 17 22 39 31 28 52 147 EGR 252 Spring 2013

  6. Calculations: Variability of the Data • sample variance, • sample standard deviation, EGR 252 Spring 2013

  7. Other Descriptors • Discrete vs Continuous • discrete: countable • continuous: measurable • Distribution of the data • “What does it look like?” EGR 252 Spring 2013

  8. Graphical Methods – Stem and Leaf Stem and leaf plot for radar data Stem Leaf Frequency 1 7 1 2 2 8 2 3 1 9 2 4 5 2 1 6 7 8 9 10 11 12 13 14 7 1 EGR 252 Spring 2013

  9. Graphical Methods - Histogram • Frequency Distribution (histogram) • Develop equal-size class intervals – “bins” • ‘Rules of thumb’ for number of intervals • 7-15 intervals per data set • Square root of n • Interval width = range / # of intervals • Build table • Identify interval or bin starting at low point • Determine frequency of occurrence in each bin • Calculate relative frequency • Build graph • Plot frequency vs interval midpoint EGR 252 Spring 2013

  10. Data for Histogram • Example: stride lengths (in inches) of 25 male students were determined, with the following results: • What can we learn about the distribution (shape) of stride lengths for this sample? EGR 252 Spring 2013

  11. Constructing a Histogram • Determining frequencies and relative frequencies EGR 252 Spring 2013

  12. Computer-Generated Histograms EGR 252 Spring 2013

  13. Relative Frequency Graph EGR 252 Spring 2013

  14. Graphical Methods – Dot Diagram • Dot diagram (text) • Dotplot (Minitab) EGR 252 Spring 2013

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