Chapter 03 - Sections 1, 2, 4 & 5

Chapter 03 - Sections 1, 2, 4 & 5 - Chapter 3...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 3 Numerically Summarizing Data Fall 2008 1 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 Fall 2008 2 Chapter 3 Section 1 Measures of Central Tendency Fall 2008 3 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 ( μ ) ● 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 ( μ ) ● 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 Fall 2008 4 Central Tendency Calculating the Arithmetic Mean ● 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 Fall 2008 5 Summation Notation Calculating the Arithmetic Mean 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 Fall 2008 6 Summation Notation Calculating the Arithmetic Mean 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 + + + = = = + + + = = & Fall 2008 7 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 μ (mu) and equals n x x n i i ∑ = = 1 N x N i i ∑ = = 1 μ x Fall 2008 8 Central Tendency ● One interpretation ● The arithmetic mean can be thought of as the center of gravity … where the yardstick balances Fall 2008 9 Central Tendency...
View Full Document

{[ snackBarMessage ]}

Page1 / 80

Chapter 03 - Sections 1, 2, 4 & 5 - Chapter 3...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online