Download EGR252S15_Chapter1_MDHpublish v2

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 1
EGR 252 Fall 2015
Slide 1
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:
17
22
39
31
28
52
147
 the sample mean, x = ?
MDH Chapter 1
EGR 252 Fall 2015
Slide 2
Calculation of Mean
 Example: The absolute error in the readings from a
radar navigation system was measured with the
following results:
17
22
39
31
28
52
147
_
 the sample mean, X
= (17+ 22+ 39 + 31+ 28 + 52 + 147) / 7
= 48
MDH Chapter 1
EGR 252 Fall 2015
Slide 3
Calculation of Median
 Example: The absolute error in the readings from a radar
navigation system was measured with the following results:
17
22
39
31
28
52
147
~
 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.
MDH Chapter 1
EGR 252 Fall 2015
Slide 4
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:
17
22
39
31
28
52
147
 sample range = Max – Min = 147 – 17 = 130
MDH Chapter 1
EGR 252 Fall 2015
Slide 5
Calculations: Variability of the Data
 sample variance,
n
s 
2
i 1
xi  x 
2
n 1

17  48  22  48 ...  147  48

2
s
2

2
6
2
 2037.3
 sample standard deviation,
s  s 2  45.14
MDH Chapter 1
EGR 252 Fall 2015
Slide 6
Other Descriptors
 Discrete vs Continuous
 discrete: countable
 continuous: measurable
 Distribution of the data
 “What does it look like?”
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0.35
0.60
0.30
0.50
0.25
0
2
4
6
8
0
2
4
6
8
0.40
0.20
0.30
0.15
0.20
0.10
0.10
0.05
0.00
0.00
0
MDH Chapter 1
2
4
6
8
EGR 252 Fall 2015
Slide 7
Graphical Methods – Stem and Leaf
Stem and leaf plot for radar data
Stem
1
2
3
4
5
6
7
8
9
10
11
12
13
14
MDH Chapter 1
Leaf
7
2
1
Frequency
1
2
2
8
9
2
1
7
1
EGR 252 Fall 2015
Slide 8
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 1
EGR 252 Fall 2015
Slide 9
Data for Histogram
 Example: stride lengths (in inches) of 25 male
students were determined, with the following
results:
28.6
26.1
28.6
26.6
29.0
Stride Length
26.5
30.0
29.7
27.3
28.6
26.8
29.5
27.0
27.3
25.7
27.1
28.5
27.0
27.3
28.8
27.8
29.3
27.3
28.0
31.4
 What can we learn about the distribution (shape)
of stride lengths for this sample?
MDH Chapter 1
EGR 252 Fall 2015
Slide 10
Constructing a Histogram
 Determining frequencies and relative frequencies
Midpoint Frequency
Relative
Frequency
Lower
Upper
24.85
26.20
25.525
2
0.08
26.20
27.55
26.875
10
0.40
27.55
28.90
28.225
7
0.28
28.90
30.25
29.575
5
0.20
30.25
31.60
30.925
1
0.04
S  25
MDH Chapter 1
EGR 252 Fall 2015
= 2/25
S  1.0
Slide 11
Computer-Generated Histograms
Excel Chart Using Bar Graph Function
Excel-Generated Histogram
Frequency
Frequency
15
10
5
15
10
5
0
0
25.525
26.875 28.225 29.575
Cell Midpoint
30.925
26.20
27.55 28.90 30.25
Bin Upper Bound
31.60
Minitab Histogram of 252dataset2
10
8
Frequency
Bin Size determined using
Sturges’ formula
= 1+3.3 log (n)
= 5.61 round to 6
6
4
2
0
MDH Chapter 1
26
EGR 252 Fall 2015
27
28
29
252dataset2
30
31
Slide 12
Relative Frequency Graph
Relative
Frequency
Relative Frequency Histogram
0.60
0.40
0.20
0.00
25.53
26.88
28.23
29.58
30.93
Cell Midpoint
MDH Chapter 1
EGR 252 Fall 2015
Slide 13
Graphical Methods – Dot Diagram
 Dot diagram (text)
 Dotplot (Minitab)
Dotplot of 252dataset2
25.6
MDH Chapter 1
26.4
27.2
28.0
28.8
252dataset2
EGR 252 Fall 2015
29.6
30.4
31.2
Slide 14
Homework and Reading
Assignment
 Reading
 Problems
 Chapter 1:
Introduction to
Statistics and Data
Analysis pg. 1- 30
MDH Chapter 1
 1.9 pg. 17
 1.18 pg. 31
EGR 252 Fall 2015
Slide 15