Calculation of Percentiles and Quartiles PDF

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Calculation of Percentiles and Quartiles First quartile also known as lower quartile = 25th percentile Second quartile also known as middle quartile = 50th percentile = median Third quartile also known as upper quartile = 75th percentile Let 0 < p < 1 To determine 100pth percentile, perform the following steps: 1. Arrange sample data X1, X2, …, .Xn in an increasing order from the lowest value to the highest value. Let the ordered data be written as X(1), X(2), …., X(n) 2. Let the order or rank of the 100pth percentile be denoted as k. Then, k = (n + 1)p and let the value of k be denoted as a.bc (a denotes the integer portion of the rank k and bc represents the first and second digit after the decimal point of rank k, respectively) 3. 100pth percentile is X(k) = X(a) + 0.bc(X(a+1) – X(a)) Note: p = 0.25 for the first quartile, p = 0.5 for the second quartile, and p = 0.75 for the third quartile. MINITAB calculates rank or order of 100pth percentile as k = np + 0.5, The difference between the value of k used by MINITAB and the one used in Step 2 above is small so long as n is not small and 0.1 < p < 0.9 Refer to the class work for the calculation of percentiles and quartiles....