Ch 6 F2014 6th Edition - 6 Descriptive Statistics CHAPTER...

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Descriptive statistics 1 6 Descriptive Statistics CHAPTER OUTLINE
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Learning Objective for Chapter 6 After careful study of this chapter, you should be able to do the following: 1. Compute and interpret the sample mean, variance, standard deviation, median, and range. 2.Explain the concepts of sample mean, variance, population mean, and variance. 3. Construct and interpret visual data displays, including stem-and-leaf display, histogram, and box plot. 4. Concept of random sampling. 5. Construct and interpret normal probability plots. 6. How to use box plots, and other data displays, to visually compare two or more samples of data. 7. How to use simple time series plots to visually display the important features of time-oriented data. 2 Chapter 6 Learning Objectives
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Numerical Summaries of Data Data are the numeric observations of a phenomenon of interest. The totality of all observations is a population . A portion used for analysis is a random sample . We gain an understanding of this collection, possibly massive, by describing it numerically and graphically, usually with the sample data. We describe the collection in terms of shape, outliers, center, and spread (SOCS). The center is measured by the mean. The spread is measured by the variance. Sec 6-1 Numerical Summaries of Data 3
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Populations & Samples Sec 6-1 Numerical Summaries of Data 4 Figure 6-3 (out of order) A population is described, in part, by its parameters , i.e., mean (μ) and standard deviation (σ). A random sample of size n is drawn from a population and is described, in part, by its statistics , i.e., mean ( x-bar ) and standard deviation ( s ). The statistics are used to estimate the parameters.
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Sample Mean Sec 6-1 Numerical Summaries of Data 5 1 2 1 2 1 If the observations in a random sample are denoted by , ,..., , the is ... (6-1) For the observations in a populatio sample mea n denoted by n n n i n i n x x x x x x x x n n N x 1 2 1 1 , ,..., , the is analogous to a probability distribution as = (6-2 population mean ) N N i N i i i x x x x f x N
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Exercise 6-1: Sample Mean Consider 8 observations ( x i ) of pull-off force from engine connectors from Chapter 1 as shown in the table. Sec 6-1 Numerical Summaries of Data 6 Figure 6-1 The sample mean is the balance point. 8 1 12.6 12.9 ... 13.1 average 8 8 104 13.0 pounds 8 i i x x
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Variance Defined Sec 6-1 Numerical Summaries of Data 7 1 2 2 2 1 If the observations in a sample are denoted by , ,..., , the is sampl e varianc (6-3) 1 For the observations e i n n i i n x x x x x s n N 1 2 2 2 2 1 1 n a population denoted by , ,..., , the , analogous to the variance of a probability distribution, is = ( population varian 6-5 ce ) N N i N i i i x x x x x f x N
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Standard Deviation Defined The standard deviation is the square root of the variance.
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