Lecture 5 - Measures of Dispersion Lecture 5 1 Definition...

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1 Measures of Dispersion Lecture - 5
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2 Definition Measures of dispersion are descriptive statistics that describe how similar a set of scores are to each other The more similar the scores are to each other, the lower the measure of dispersion will be The less similar the scores are to each other, the higher the measure of dispersion will be In general, the more spread out a distribution is, the larger the measure of dispersion will be
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3 Measures of Dispersion Which of the distributions of scores has the larger dispersion? 0 25 50 75 100 125 1 2 3 4 5 6 7 8 9 10 0 25 50 75 100 125 1 2 3 4 5 6 7 8 9 10 The upper distribution has more dispersion because the scores are more spread out That is, they are less similar to each other
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4 Measures of Dispersion Following are the main measures of dispersion: The range The interquartile range (IQR) Mean absolute deviation Variance / standard deviation
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5 The Range The range is defined as the difference between the largest score in the set of data and the smallest score in the set of data, X L - X S What is the range of the following data: 4 8 1 6 6 2 9 3 6 9 The largest score (X L ) is 9; the smallest score (X S ) is 1; the range is X L - X S = 9 - 1 = 8
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6 When To Use the Range The range is used when you have ordinal data or you are presenting your results to people with little or no knowledge of statistics The range is rarely used in scientific work as it is fairly insensitive It depends on only two scores in the set of data, X L and X S Two very different sets of data can have the same range: 1 1 1 1 9 vs 1 3 5 7 9
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