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ECON 2B03 (45)
Lecture 6

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McMaster University
Jeff Racine

Lecture 6 Chebyshev’s Theorem Chebyshev’s Theorem is an empirical rule that applies to all distributions, not only the Normal distribution Regardless of the shape of a population’s frequency distribution, the proportion of observations falling within k standard deviations of the mean is at least (given that k equals 1 or more); 1 ±kσof μ≥1− 2 Proportion falling within k Example (Chebyshev’s Theorem) At least 75% of all observations lie within k= 2 standard deviations of the mean Coefficient of Variation Used to compare degrees of dispersion among data sets Ratio of the standard deviation to the arithmetic mean In R use sd()/ mean() CHAPTER III Origins of Data Data can originate in a number of ways Internal Data Created as by-products of regular activities Example (Internal Data) Customer, employee, production records; government records External Data (typical source for this course) Created by entities other than the person, firm, or government that wants to use the data Example (External Data) Print sources, CD-ROMs, web sites In the past, users were limited to print data (e.g., print and CDROM) Frequently expensive Useful for transferring to computer applications The Internet is an exceptionally efficient source for data Sampling Versus Census Taking A census is a complete survey of every member in the population A sample is a partial survey in which data is collected for only a subset of the population Reasons for sampling versus conducting a census Expense can be prohibitive Speed of response Impossible. For example, we may have an infinite population (i.e., observations occur from an infinite or recurring process) Destructive sampling (e.g., lifetime of light bulb, safety of automobile [destroys all output]) Accuracy can, oddly enough, be better (e.g., higher quality information results via hiring fewer persons who can be better trained, say) Types of Samples: Nonprobability Nonprobability Sample: occurs when a sample is taken from an existing population in a haphazard fashion without the use of some randomizing device assigning each member a known (positive) probability of selection Voluntary response sample (e.g., phone survey [self-selection issue]) Convenience sample (e.
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