Lecture 4_variability

# Lecture 4_variability - Measures of Variability Quantifying...

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8/26/2010 1 Measures of Variability: Quantifying the Spread of Scores in the Data 1 0 M 0 M An Example • The mean of both of these distributions of scores is zero. Are the distributions skewed? What are the values of the median and mode in the distributions? Why? How do the two graphs differ? 2 0 M 0 M An Example • The range of scores in the two graphs is not the same. What appears to be the lowest score in the left distribution? The highest? How does this differ from the distribution on the right? What might this say about similarity of scores in each distribution? 3

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8/26/2010 2 Another Example • Consider scores on the same test from two different statistics classes: Class 1 : 80%, 80%, 80%, 80%, 80% Class 2 : 60%, 70%, 80%, 90%, 100% • What is the mean of the Class 1 test scores? The Class 2 test scores? 4 Another Example Cntd… • The mean of the two sets of scores from the different classes are identical… • But would you characterize the sets of scores as the same if someone asked you to describe them? • How do the scores differ? 5 Why is Variability Important? • Measures of central tendency cannot fully differentiate among and/or describe different sets of scores • Different sets of scores can have the exact same values of central tendency measures even if the variety of the scores in each dataset are nothing alike – Why might it be of interest to know the variety of scores that occur in a dataset? 6
8/26/2010 3 Defining Variability Variability is the degree to which scores are spread out or clustered together around the most typical score in the data • To accurately describe a distribution, we will need to estimate both measures of central tendency and variability – Together these measures give us a sense of the most typical score in the data and the variety of scores in the data 7 8 Normal Distribution Leptokurtic Distribution Platykurtic Distribution Measures of Variability • There are four measures of variability: Range Variation Variance Standard deviation • The concept of variability is particularly important to inferential statistics – Lower variability in a set of scores will allow us to have greater confidence in the sample statistics that we obtain as estimates of the true population parameters 9

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8/26/2010 4 The Range • The range is a single number defined as the distance between the lowest and the highest score in the data: 10 Range = Highest Score – Lowest Score in the data in the data The Range • What is the range of the following scores? 1
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Lecture 4_variability - Measures of Variability Quantifying...

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