Stats 309 4-1 to 4-2

# Stats 309 4-1 to 4-2 - Section 4.1 Measures of Central...

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A p arameter is a descriptive measure of a p opulation . A s tatistic is a descriptive measure of a s ample . Section 4.1 Measures of Central Location Recall: There are three measures used to describe the center of a data set: the mean, median and mode. We will discuss how to calculate these for any population or sample. However, in most applications, populations are virtually infinitely large, making parameters impractical to calculate.

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Summation Notation is used in several statistical formulas. In order to use summation notation we label the observations in a sample where is the 1 st observation, is the second observation and n is the sample size. The sigma symbol is used to denote a sum: Consider the following sample data. Mark’s MthSc 309 test scores were 95, 89, 92 and 94. Find: This means to sum the x i ’s for i =1, i =2, i =3 and i =4. 1 2 3 n x ,x ,x ,. ..,x 1 x 2 x e 4 1 i i x = 4 1 2 3 4 1 95 89 92 94 370 i i x x x x x = = + + + = + + + =
The Arithmetic Mean is usually referred to as the mean and is commonly referred to as the average. The mean is computed by summing the observations and dividing by the number of observations. Population Mean Sample Mean The population mean is denoted by the Greek letter mu ( μ ). The sample mean is denoted by the symbol (x bar). Notice the formulas are identical except for the fact that the population size is denoted by N and the sample size is denoted by n. 1 N i i x N = = x 1 n i i x x n = =

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Example 1: A sample of ten adults was asked to report the number of hours they spent on the Internet the previous month. The results are listed below: 0 7 12 5 33 14 8 0 9 22 Calculate the sample mean, using proper notation: 1 n i i x x n = = 10 1 10 i i x = = 1 2 3 10 ... 10 x x x x + + + + = 0 7 12 5 33 14 8 0 9 22 10 + + + + + + + + + = 110 10 = 11 x =
is the middle value when the measurements are arranged from lowest to highest. -For an odd number of measurements, the median is the specific value in the middle. -For an even number of measurements, the median is the average of the two middle values. -Not sensitive to extreme values. -Can be used with quantitative data. The mode is the measurement that occurs most often (with the highest frequency). -It is possible to have more than one mode. -It is also possible to have no mode. -Can be used with both quantitative and qualitative data.

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## This note was uploaded on 04/09/2008 for the course MTHSC 309 taught by Professor Cathydavis during the Spring '08 term at Clemson.

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Stats 309 4-1 to 4-2 - Section 4.1 Measures of Central...

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