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Published byMarlene Parks Modified over 9 years ago
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COMPUTATIONAL FORMULAS AND IQR’S
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Compare the following heights in inches: BoysGirls 7261 7464 7065 6866 6968 7067 6865 6963 6762 7065 7166 67 64 66
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Objective Calculate standard deviation, variance and IQR.
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Relevance To be able to analyze a set of data and see how far each value is above or below the mean of the set.
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Computational Formula This is an easier computational formula that contains no rounding.
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Example – Find Var and St Dev 7 8 22 34 42
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You Try One! 4 8 12 18 22 34 38
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Is the standard deviation affected by outliers? 5 7 5 8 9 5 7 5 8 29
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The standard deviation IS sensitive to extreme values.
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67 65 68 70 74 60 61 64 67 68 The following data represents the heights of some students in my class. a.Find the mean & standard deviation. b.What % are within 1 standard deviation of the mean? ( ) c.What % are within 2 standard deviations f the mean? ( )
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IQR – Interquartile Range This is the measure of variability that is not affected by outliers. It is based on quartiles.
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25% - This is the median of the lower ½ of the sample. - This is the median. - This is the median of the upper ½ of the sample.
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18242527 29303334 ) ) ( ( Q1 = 24.5Q3 = 31.5 IQR = 31.5 – 24.5 = 7
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Find IQR 1213161822242740 Q1 = 14.5 Q3 = 25.5 IQR = 25.5 – 14.5 = 11
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Find IQR 8101114162022262832 IQR = 15
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Find IQR 456671022 IQR = 15
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If normal distribution – then you can estimate the standard deviation with the IQR. *Can also be use to check to see if a distribution is normal – if much larger then it’s skewed.
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Which Measure Should You Report? ShapeCentral Tendency Dispersion (Spread) SymmetricMeanStandard Deviation Skewed Left or Right MedianIQR NOTE: When told to “describe the distribution” you will give the shape, the center and the spread of the distribution using the above categories as a guideline.
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Homework Worksheet Use the new formula to compute the standard deviation. Now – time for the lab!
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