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# lec25 - Other descriptive statistics Review Descriptive...

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Other descriptive statistics Review: Descriptive statistics, inferential statistics, sample/population mean, sample/population variance, sample/population median, range Population quantile: A p-quantile of a population is a number x that solves equations P ( X < x ) p, P ( X > x ) 1 - p Sample quantile: A sample p-quantile is any number that exceeds at most 100 · p % of the sample and is exceeded by at most 100(1 - p )% of the sample. Percentile: A p -quantile is also called a 100 p th percentile. Quartile: The 1st, 2nd and 3rd quartiles are the 25th, 50th, and 75th percentiles. They split a population or a sample into four parts. A median is at the same time a 0 . 5 -quantile, 50 th percentile, and 2nd quartile. 1

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Example: Example: The CPU time for randomly chosen tasks are 70 , 36 , 43 , 49 , 82 , 48 , 34 , 62 , 35 , 15 with ordered sample 15 , 34 , 35 , 36 , 43 , 48 , 49 , 62 , 70 , 82 The first quartile: for p = 0 . 25 and n = 10 , so 25% of the sample equals to np = 2 . 5 and 75% of the sample is n (1 - p ) = 7 . 5 . From the ordered sample, we see only the 3rd element, 35 , has no more than 2 . 5 observations to the left and no more than 7.5 observations to the right of it. Hence, the first quartile ˆ Q 1 = 35 . The third quartile is ˆ Q 3 = 62 . 2
Other descriptive statistics (Cont’d) Interquartile range (IQR): is the difference between the first and the third quartiles IQR = Q 3 - Q 1 It measures the variability of the data and not affected by outliers significantly. In practice, outliers maybe a real serious problem that it is hard to avoid.

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lec25 - Other descriptive statistics Review Descriptive...

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