1. JMB Chapter 1EGR 252.001 Spring 2010 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

2. JMB Chapter 1EGR 252.001 Spring 2010 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 = ? 17 22 39 31 28 52 147

3. JMB Chapter 1EGR 252.001 Spring 2010 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 = (17+ 22+ 39 + 31+ 28 + 52 + 147) / 7 = 48 17 22 39 31 28 52 147

4. JMB Chapter 1EGR 252.001 Spring 2010 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: 17 22 28 31 39 52 147  n odd median = x (n+1)/2, → 31  n even median = (x n/2 + x n/2+1 )/2 17 22 39 31 28 52 147 ~

5. JMB Chapter 1EGR 252.001 Spring 2010 Slide 5 Descriptive Statistics: Variability  A measure of variability  (Recall) Example: The absolute error in the readings from a radar navigation system was measured with the following results:  sample range: Max - Min 17 22 39 31 28 52 147

6. JMB Chapter 1EGR 252.001 Spring 2010 Slide 6 Calculations: Variability of the Data  sample variance,  sample standard deviation,

7. JMB Chapter 1EGR 252.001 Spring 2010 Slide 7 Other Descriptors  Discrete vs Continuous  discrete: countable  continuous: measurable  Distribution of the data  “What does it look like?”

8. JMB Chapter 1EGR 252.001 Spring 2010 Slide 8 Graphical Methods – Stem and Leaf Stem and leaf plot for radar data StemLeafFrequency 171 2282 3192 4 521 6 7 8 9 10 11 12 13 1471

9. JMB Chapter 1EGR 252.001 Spring 2010 Slide 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

10. JMB Chapter 1EGR 252.001 Spring 2010 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 of stride lengths for this sample? Stride Length 28.6026.5030.0027.1027.80 26.1029.7027.3028.5029.30 28.60 26.8027.0027.30 26.6029.5027.0027.3028.00 29.0027.3025.7028.8031.40

11. JMB Chapter 1EGR 252.001 Spring 2010 Slide 11 Constructing a Histogram  Determining frequencies and relative frequencies LowerUpperMidpointFrequency Relative Frequency 24.8526.2025.52520.08 26.2027.5526.875100.40 27.5528.9028.22570.28 28.9030.2529.57550.20 30.2531.6030.92510.04

12. JMB Chapter 1EGR 252.001 Spring 2010 Slide 12 Computer-Generated Histograms

13. JMB Chapter 1EGR 252.001 Spring 2010 Slide 13 Relative Frequency Graph

14. JMB Chapter 1EGR 252.001 Spring 2010 Slide 14 Graphical Methods – Dot Diagram  Dot diagram (text)  Dotplot (Minitab)