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### High School Mathematics14.23 Partition Values for Discrete Variables (Percentiles, Quartiles and Interquartile Range)

 Quartiles Just as one median divides the data into two subgroups, three quartiles divides the data into 4 quarters. The three quartiles are normally represented by the points Q1, Q2, Q3 The lower quartile is denoted by Q1 and the upper quartile by Q3. The second quartile Q2 is the same as the median. Positions of the Quartile Lower Quartile Q1 (25 th percentile) : (n+1)/4 Upper Quartile Q3 : 3(n+1)/4 The difference between the upper and the lower quartile value is called the Interquartile range Example Find Q1, Q3 in the following series. 33, 32, 55, 47, 21, 50, 27, 12, 68, 49, 40, 17, 44, 48, 62 Solution Arranging in ascending order, we get 12, 17, 21, 27, 32, 33, 40, 44, 47, 48, 49, 50, 55, 62, 68 Here n = 15 Q1 (25 th percentile) = Size of [(n+1)/4] th item = Size of (15+1)/4 = size of the 4 th item So Q1 = 27 Q3 (75 percentile) = Size of [3(n+1)/4] th item = Size of [3(15+1)]/4 = size of the 12 th item So Q3 = 50 68 = 100 percentile
 Q 1: Find the lower quartile for the following data: 15, 17, 18, 25, 28, 29, 50, 75, 79, 81, 82.79181715 Q 2: Calculate the lower and the upper quartile for the following series. 33, 32, 55, 47, 21, 54, 31, 12, 68, 49, 40, 17, 44, 48, 62 Q1=33,Q3=50Q1=32,Q3=55Q1=31,Q3=54Q1=12,Q3=54 Question 3: This question is available to subscribers only! Question 4: This question is available to subscribers only!