JMB Chapter 1 EGR 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
JMB Chapter 1 EGR 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
JMB Chapter 1 EGR 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
JMB Chapter 1 EGR 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 = (xn/2 + xn/2+1)/2
17
22
39
31
28
52
147
~
JMB Chapter 1 EGR 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
JMB Chapter 1 EGR 252.001 Spring 2010 Slide 6
Calculations: Variability of the Data
sample variance,
sample standard deviation,
n
i
i
n
xxs
1
22
1
14.452 ss
3.2037
6
48147...48224817 2222
s
JMB Chapter 1 EGR 252.001 Spring 2010 Slide 7
Other Descriptors Discrete vs Continuous
discrete: countable continuous: measurable
Distribution of the data “What does it look like?”
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 2 4 6 8
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 2 4 6 8
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0 2 4 6 8
JMB Chapter 1 EGR 252.001 Spring 2010 Slide 8
Graphical Methods – Stem and Leaf
Stem and leaf plot for radar dataStem Leaf Frequency1 7 12 2 8 23 1 9 245 2 167891011121314 7 1
JMB Chapter 1 EGR 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
JMB Chapter 1 EGR 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
28.60 26.50 30.00 27.10 27.80
26.10 29.70 27.30 28.50 29.30
28.60 28.60 26.80 27.00 27.30
26.60 29.50 27.00 27.30 28.00
29.00 27.30 25.70 28.80 31.40
JMB Chapter 1 EGR 252.001 Spring 2010 Slide 11
Constructing a Histogram Determining frequencies and relative frequencies
Lower Upper Midpoint FrequencyRelative Frequency
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
JMB Chapter 1 EGR 252.001 Spring 2010 Slide 12
Computer-Generated Histograms
Excel Chart Using Bar Graph Function
0
5
10
15
25.525 26.875 28.225 29.575 30.925Cell Midpoint
Freq
uenc
y
Excel-Generated Histogram
0
5
10
15
26.20 27.55 28.90 30.25 31.60Bin Upper Bound
Freq
uenc
y
252dataset2
Frequency
313029282726
10
8
6
4
2
0
Minitab Histogram of 252dataset2
JMB Chapter 1 EGR 252.001 Spring 2010 Slide 13
Relative Frequency Graph
Relative Frequency Histogram
0.00
0.20
0.40
0.60
25.53 26.88 28.23 29.58 30.93
Cell Midpoint
Rel
ativ
e
Fre
qu
ency
JMB Chapter 1 EGR 252.001 Spring 2010 Slide 14
Graphical Methods – Dot Diagram
Dot diagram (text) Dotplot (Minitab)
252dataset231.230.429.628.828.027.226.425.6
Dotplot of 252dataset2