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
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JMB Chapter 1EGR 252.001 Spring 2010 Slide 1 Probability and Statistics for Engineers Descriptive Statistics Measures of Central Tendency Measures.
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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?”