Chapter 6

# Chapter 6 - Chapter 6 Descriptive Statistics 1 6.1 Random...

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Chapter 6 Descriptive Statistics 1

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2 6.1 Random Samples Random Sampling: A sample is selected in such a way that every possible sample of the same size n will have an equal chance of being selected. Random sample: A random sample of size n would be a collection of independent random variables X 1, …, X n , each with the same distribution.
Describing Samples We can describe the values in a sample in two manners: - graphically - numerically 3

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6. 2 Describing Samples Graphically Some of the frequently used graphical methods are stem-and-leaf plots (or stem- plots), histograms, cumulative distribution plots, and boxplots (or box-and-whisker plots). For bivariate data, scatterplots can also be used. 4
Stem and Leaf Diagrams A stem and leaf diagram allows us to observe the shape of the data and keep the original data at the same time. Dataset: 61, 63, 64, 65, 65, 66, 70, 71, 71, 73, 75, 77, 78, 78, 79, 81, 83, 84, 84, 87, 88, 88, 92, 93, 95 5

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When a stem is displayed only once, the leaves can take on the values from 0-9. (See figure A on previous slide.) When a stem is displayed twice, one stem is associated with the leaves 0-4 and the other stem is associated with the leaves 5-9. (See figure B on previous slide.) Constructing a Stem and Leaf Diagram: 6
Histograms A histogram is a graphical measure that divides the data into intervals. It can be a graphical measure of a frequency distribution. Frequency Distribution – A listing that pairs each value of a variable with its frequency. 7

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Example of an Ungrouped Frequency Distribution: Data: 5, 3, 4, 5, 7, 6, 4, 8, 7, 6, 6 Score on quiz f 1 0 2 0 3 1 4 2 5 2 6 3 7 2 8 1 8
Example of an Ungrouped Frequency Histogram: Score Frequency 8 7 6 5 4 3 3.0 2.5 2.0 1.5 1.0 0.5 0.0 Histogram of Score 9

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Example of a Grouped Frequency Distribution and Histogram: Data: 5, 3, 4, 5, 7, 6, 4, 8, 7, 6, 6 Score on quiz f 1 - 2 0 3 - 4 3 5 - 6 5 7 - 8 3 Score Frequency 7-8 5-6 3-4 1-2 5 4 3 2 1 0 Histogram of Score 10
– A listing that pairs each value of a variable with its frequency divided by the number of observations. Note: Rel. Freq. must sum to 1.

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Chapter 6 - Chapter 6 Descriptive Statistics 1 6.1 Random...

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