Chapter 6 - 6-1 Numerical SummariesDefinition: Sample...

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Unformatted text preview: 6-1 Numerical SummariesDefinition: Sample Mean6-1 Numerical Summaries Example 6-16-1 Numerical Summaries FulcrumThe sample mean as a balance point for a system of weights.6-1 Numerical Summaries Population MeanFor a finite population with Nmeasurements, the mean isThe sample meanis a reasonable estimate of the population mean.6-1 Numerical Summaries Definition: Sample VarianceWhy (n-1)?(1)xitend to be closer to the sample mean x than the true mean μ. To compensate for that and avoid obtaining a variance that’s often smaller than the true variance σ2we use (n-1). (2)The number of degrees of freedom of the sum is (n-1).6-1 Numerical Summaries Example 6-2•The table below displays the quantities needed for calculating the sample variance and sample standard deviation for the pull-off force data.6-1 Numerical Summaries Example 6-26-1 Numerical Summaries Computation of s26-1 Numerical Summaries Population VarianceWhen the population is finite and consists of N values, we may define the population varianceasThe sample varianceis a reasonable estimate of the population variance.6-1 Numerical Summaries Definition6-2 Stem-and-Leaf Diagrams •A stem-and-leaf diagram is a good way to obtain an informative visual of a data set x1, x2, …, xn, where each number xiconsists of at least two digits. •To construct a stem-and-leaf diagram, use the following steps: 6-2 Stem-and-Leaf Diagrams 6-2 Stem-and-Leaf Diagrams Stem-and-leaf diagram for the compressive strength data in Table 6-2. Units:Stem: Tens and hundreds (psi)Leaf: Ones (psi)6-2 Stem-and-Leaf Diagrams •The last column is the frequency count of the number of leaves associated with each stem.•Inspection of this display reveals that most of the compressive strength lie between 110 and 200 psi and that a central value is somewhere between 150 and 160.•The stem-and-leaf diagram enables us to determine quickly some features of the data that were not immediately obvious in the original display in the table.6-2 Stem-and-Leaf Diagrams Example 6-5•Too few stems, moderate number of stems, or too many?It does not provide much information 6-2 Stem-and-Leaf Diagrams Example 6-5•Too few stems, moderate number of stems, or too many?...
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This note was uploaded on 10/12/2011 for the course STATISTICS 101 taught by Professor Nazim during the Spring '10 term at Qatar University.

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Chapter 6 - 6-1 Numerical SummariesDefinition: Sample...

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