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Unformatted text preview: Chapter 3 Numerically Summarizing Data Overview How could we describe or summarize the distribution of data in numeric ways? How could we describe or summarize the distribution of data in numeric ways? In this chapter, we will discuss Measures of the center of a set of data Measures of the spread of a set of data Ways of using these numeric measures to analyze data sets How could we describe or summarize the distribution of data in numeric ways? In this chapter, we will discuss Measures of the center of a set of data Measures of the spread of a set of data Ways of using these numeric measures to analyze data sets This complements what we did in Chapter 2 where we organized and summarized data in more visual ways Chapter 3 Section 1 Measures of Central Tendency Populations vs Samples Analyzing populations versus analyzing samples Analyzing populations versus analyzing samples For populations We know all of the data Descriptive measures of populations are called parameters Parameters are often written using Greek letters ( ) Analyzing populations versus analyzing samples For populations We know all of the data Descriptive measures of populations are called parameters Parameters are often written using Greek letters ( ) For samples We know only part of the entire data Descriptive measures of samples are called statistics Statistics are often written using Roman letters ( ) x Central Tendency Learning objectives The arithmetic mean of a variable The median of a variable The mode of a variable Identifying the shape of a distribution 1 2 3 4 Central Tendency The arithmetic mean of a variable is often what people mean by the average add up all the values and divide by the number of measurements in the data set Compute the arithmetic mean of 6, 1, 5 Add up the three numbers and divide by 3 (6 + 1 + 5) / 3 = 4.0 The arithmetic mean is 4.0, one more decimal place than the data Summation Notation Used to simplify summation instructions Each observation in a data set is identified by a subscript x 1 , x 2 , x 3 , x 4 , x 5 , . x n Notation used to sum the above numbers together is n n i i x x x x x x + + + + + = = 4 3 2 1 1 Summation Notation Data set: 1, 2, 3, 4 Are these the same? and = 4 1 2 i i x 2 4 1 = i i x 2 2 2 2 2 1 2 3 4 4 1 1 4 9 16 30 i i x x x x x + + + = = = + + + = ( 29 1 2 3 4 2 4 2 2 2 1 1 2 3 4 10 100 i i x x x x x + + + = = = + + + = = & Central Tendency The mean is an arithmetic average of the elements of the data set The mean of a sample of n measurements is denoted by and equals If the data are from a population , the mean is denoted by (mu) and equals n x x n i i = = 1 N x N i i = = 1 x Central Tendency One interpretation The arithmetic mean can be thought of as the center of gravity where the yardstick balances Central Tendency...
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This note was uploaded on 08/04/2008 for the course STAT 250 taught by Professor Sims during the Spring '08 term at George Mason.
 Spring '08
 sims
 Statistics

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