Page 222 - Applied statistics and probability for engineers

200 Chapter 6/Descriptive Statistics

Learning Objectives
After careful study of this chapter, you should be able to do the following:

1. Compute and interpret the sample mean, sample variance, sample standard deviation, sample
median, and sample range
2. Explain the concepts of sample mean, sample variance, population mean, and population variance
3. Construct and interpret visual data displays, including the stem-and-leaf display, the histogram, and
the box plot
4. Explain the concept of random sampling
5. Construct and interpret normal probability plots
6. Explain how to use box plots and other data displays to visually compare two or more samples of data
7. Know how to use simple time series plots to visually display the important features of time-oriented data
8. Know how to construct and interpret scatter diagrams of two or more variables

6-1 Numerical Summaries of Data

Well-constructed data summaries and displays are essential to good statistical thinking,
because they can focus the engineer on important features of the data or provide insight about
the type of model that should be used in solving the problem. The computer has become an
important tool in the presentation and analysis of data. Although many statistical techniques
require only a handheld calculator, this approach may require much time and effort, and a
computer will perform the tasks much more efi ciently.
Most statistical analysis is done using a prewritten library of statistical programs. The user
enters the data and then selects the types of analysis and output displays that are of interest.
Statistical software packages are available for both mainframe machines and personal com-
puters. We will present examples of typical output from computer software throughout the

book. We will not discuss the hands-on use of speciic software packages for entering and
editing data or using commands.

We often ind it useful to describe data features numerically. For example, we can charac-
terize the location or central tendency in the data by the ordinary arithmetic average or mean.
Because we almost always think of our data as a sample, we will refer to the arithmetic mean
as the sample mean.

Sample Mean
If the n observations in a sample are denoted by x , x , … , x , the sample mean is
n
1
2
n
∑
− x + x + … + x n i = 1 x i
x = 1 2 = (6-1)
n n

Example 6-1 Sample Mean Let’s consider the eight observations on pull-off force collected from the proto-
type engine connectors from Chapter 1. The eight observations are x 1 = 12 6, x 2 = 12 9, x 3 = 13 4,
.
.
.
x 4 = 12 3, x 5 = 13 6, x 6 = 13 5, x 7 = 12 6, and x 8 = 13 1. The sample mean is
.
.
.
.
.
8
∑
x + x +⋯ + x i 12 6 . +12 9 . +⋯ +13 1 . 104
x = 1 2 x n = i =1 = = = 13 pounds
.0
n 8 8 8