(4)Sec2.4-2.6

(4)Sec2.4-2.6 - Continued from Order Statistics Explanation...

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Continued from Order Statistics
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Explanation of Quantiles We are given a data set as the sample, 1 st Quartile, Q 1 , is the 25% quantile which means 25% of the data from the sample will be less than or equal Q 1 , Median, M e , is the 50% quantile which means half of the data from the sample will be less than or equal M e , 3 rd Quartile, Q 3 , is the 75% quantile which means 75% of the data from the sample will be less than or equal Q 3 ,
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Similarly, 90% quantile, Q 0.9 means 90% of the data from the sample will be less than or equal Q 0.9 . In general, for any percentage p, 0<p<1, p th quantile Q p means 100p% of the data from the sample will be less than or equal Q p . So we develop the formula based on this definition for quantiles as following: Q p =X ([K]) +{K}(X ([k]+1) – X ([K]) ) where K=(n+1)p, 0<p<1, and [K] is the integer part of number K and {K} is the fractional part of the number K, so {K}=K-[K].
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Quantile of X Percent 6 5 4 3 2 1 100 80 60 40 20 0 50% 90% 25% 75% Q1 Me Q3 Qp, p=90% Empirical CDF of 2.4016
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Dispersion which is a useful measure of dispersion when there are outliers in the sample. which is a dimensionless index used to compare the variability
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(4)Sec2.4-2.6 - Continued from Order Statistics Explanation...

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