Engineering Fundamentals and Problem Solving, 6e

Chapter 10Statistics

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter Objectives

•Analyze a wide variety of data sets using descriptive techniques (mean, mode, variance, standard deviation, and correlation)

•Learn to apply the appropriate descriptive statistical techniques in a variety of situations

•Create graphical representations of individual and grouped data points with graphs and histograms

2

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Descriptive Statistics•Used to summarize or describe important

features of a data set

•Parameters are calculated from available observations

•Engineers generally contend with samples rather than entire populations of data

3

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Measures of Central Tendency or Average

•MEDIAN – “Middle” value in a sample

•MODE – The most common value in the sample (there may be more than one mode)

•MEAN – Arithmetic average

n

xx i

4

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Measures of Variation

•Represent the amount of disparity (dispersal, scatter) between the data points and the mean

•Variance

•Standard Deviation

Note: n-1 is the number of degrees of freedom left after calculating n

1

)( 222

n

xxs i

2ss

5

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

6

Example Problem 10.2 •Interstate Safety Corridors are established on certain roadways with a propensity for strong cross winds, blowing dust, and frequent fatal accidents.

•A driver is expected to turn on the headlights and pay special attention to the posted speed limit in these corridors.

•In one such Safety Corridor in northern New Mexico, the posted speed limit is 75 miles per hour.

•The Department of Public Safety set up a radar checkpoint and the actual speed of 36 vehicles that passed the checkpoint is shown in the Table below.

Example – Measures of Variation

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Actual speeds of cars in Safety Corridor 70 78 70 80 86 7685 69 68 61 81 8071 82 69 71 62 7175 76 85 72 63 7265 90 77 89 76 7066 78 91 69 80 92

7

Example – cont’d

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

a.) Make a frequency distribution table using 5 as a class width (e.g. 60.0 – 64.9)b.) Construct a histogram

Interval Frequency

60-64.9 3

65-69.9 6

70-74.9 8

75-79.9 7

80-84.9 5

85-89.9 4

90-94.5 3

8

Example – cont’d

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

c) The mean

d) The standard deviation

e) The variance

0825.70

3715.8)35(36

)2716()207360(36

)1(

)()(

44.7536

2716

2

2/122/122

nn

xxn

n

xx

ii

i

9

Example – cont’d