4_Variability

4_Variability - Descriptive Statistics Measures of...

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Descriptive Statistics Measures of Variability You should be able to . . . • Define and compute the: – Range – Variance • Parameter and statistic – Standard deviation • Parameter and statistic • Define and explain bias
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• We have discussed measures of central tendency • Now we need measures to describe the degree to which observations: cluster together or differ or deviate
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Measures of Variability • Measures that indicate the degree of difference among observations Range • A measure of variability that is the distance from the lowest score to the highest score • Range = (highest X - lowest X) + 1
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Example Distribution • What is the range? 230 200 200 150 140 130 130 130 100 80 Example Distribution • What is the range? 230 200 200 150 140 130 130 130 100 80
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Example Distribution • What is the range? • (230 - 80) + 1 = 151 230 200 200 150 140 130 130 130 100 80 Range
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Problems with the range • Based on only two observations • As number of observations increases, range increases WHY? • There is an increased probability of extreme values 44 46 42
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44 50 46 58 43 42 40 Interquartile Range • Range for the middle 50% of the observations – Chop off top 25% of observations – Chop off bottom 25% of observation
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Interquartile Range Procedure for determining IQR • 1. Order observations from least to most • 2. Find positions in the distribution that divide observations into quarters – (number of observations +1) / 4 • Now we can remove the top and bottom quarters
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Procedure for determining IQR • 3. Count from the bottom up for first quartile • 4. Count from the top down for third quartile • 5. IQR = number at top of third quartile - number at top of first quartile Example Distribution • What is the IQR? 230 200 200 150 140 130 130 130 100 80
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Example Distribution • What is the IQR? • (10+1)/4 2.75 230 200 200 150 140 130 130 130 100 80 Example Distribution • What is the IQR? • (10+1)/4 2.75 230 200 200 150 140 130 130 130 100 80 The position between the 2 nd and 3 rd scores
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Example Distribution • What is the IQR? • (10+1)/4 2.75 230 200 200 150 140 130 130 130 100 80 The position between the 2 nd and 3 rd scores Example Distribution • What is the IQR? • (10+1)/4 2.75 230 200 200 150 140 130 130 130 100 80 200 115
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Example Distribution • What is the IQR? • (10+1)/4 2.75 • 200 - 115 = 85 230 200 200 150 140 130 130 130 100 80 200 115 Advantage of IQR over range: • Not sensitive to extreme values
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• Range and IQR define variability based on two values • We could also describe variability by describing how much each
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4_Variability - Descriptive Statistics Measures of...

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