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Cards In This Set
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Numbers which describe how “spread out” a set of data is
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Measures of variability
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Examples of variability measures
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– Range– Deviation– Variance– Standard Deviatio
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Length of the smallest interval that contains all the data
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Range
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(Largest value) – (Smallest value =
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Range
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Range is sensitive to
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• Sample size: small samples = less range• Extreme score |
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Measure of distance between the first and third quartile |
Interquartile Range (IQR |
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Special kind of range that includes just the middle 50% of values
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Interquartile range (IQR)
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Benefits of interquartile range
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• Less affected by extreme values• Also helpful for identifying outlier |
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– Positions in a range of values representing multiples of 25%• Median = 2ndquartile• 50% of scores fall below median (Q2); 50% scores abov |
Quartiles
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• 25% of scores fall below Q1; 75% abov |
First quartile (Q1)
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• 75% of scores fall below Q3; 25% above
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Third quartile (Q3)
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What do you do if median is a fraction
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Round down to the nearest whole number
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How to calculate the IQR
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1. Find the median (2nd quartile) location2. Find quartile location Quartile location = (median location + 1)/23. Find 1st and 3rd quartile 4. IQR = distance between Q1 and Q3 (Q3 – Q1) |
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Extreme values that don’t “fit” with the rest of the data
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Outliers
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Rule of thumb for finding outliers using IQR
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Scores > Q3 + (1.5 x IQR) are high end outliers• e.g., 36 + (1.5 x 6.5) = 45.75– Scores < Q1 - (1.5 X IQR) are low end outliers• e.g., 29.5 – (1.5 x 6.5) = 19.75
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