MDH Chapter 1EGR 252 Fall 2015 Slide 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

MDH Chapter 1EGR 252 Fall 2015 Slide 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 = ?

MDH Chapter 1EGR 252 Fall 2015 Slide 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 = ( ) / 7 =

MDH Chapter 1EGR 252 Fall 2015 Slide 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:  n odd median = x (n+1)/2, → 31  n even median = (x n/2 + x n/2+1 )/2  If n=8, median is the average of the 4 th and 5 th data values ~

MDH Chapter 1EGR 252 Fall 2015 Slide 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 =

MDH Chapter 1EGR 252 Fall 2015 Slide 6 Calculations: Variability of the Data  sample variance,  sample standard deviation,

MDH Chapter 1EGR 252 Fall 2015 Slide 7 Other Descriptors  Discrete vs Continuous  discrete: countable  continuous: measurable  Distribution of the data  “What does it look like?”

MDH Chapter 1EGR 252 Fall 2015 Slide 8 Graphical Methods – Stem and Leaf Stem and leaf plot for radar data StemLeafFrequency

MDH Chapter 1EGR 252 Fall 2015 Slide 9 Graphical Methods - Histogram  Frequency Distribution (histogram)  Develop equal-size class intervals – “bins”  ‘Rules of thumb’ for number of intervals  Less than 50 observations 5 – 7 intervals  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

MDH Chapter 1EGR 252 Fall 2015 Slide 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? Stride Length

MDH Chapter 1EGR 252 Fall 2015 Slide 11 Constructing a Histogram  Determining frequencies and relative frequencies LowerUpperMidpointFrequency Relative Frequency  25  1.0 = 2/25

MDH Chapter 1EGR 252 Fall 2015 Slide 12 Computer-Generated Histograms Bin Size determined using Sturges’ formula = log (n) = 5.61 round to 6

MDH Chapter 1EGR 252 Fall 2015 Slide 13 Relative Frequency Graph

MDH Chapter 1EGR 252 Fall 2015 Slide 14 Graphical Methods – Dot Diagram  Dot diagram (text)  Dotplot (Minitab)

Homework and Reading Assignment  Reading  Chapter 1: Introduction to Statistics and Data Analysis pg  Problems  1.9 pg. 17  1.18 pg. 31 MDH Chapter 1EGR 252 Fall 2015 Slide 15