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12, 13, 16, 17, 20 5 data items so the median is the 3rd item i.e 16 So the upper quartile is 16 Finding the Upper and Lower Quartiles for itemised data Case1 – an even number of data items Split the data up into a lower and upper half and find the median of each half. Ex. Marks out of 20 for a test are: 1,3,4,7,8,12,13,16,17,20 10 marks so split into two groups of 5. The median of each group can be found using Median = (n + 1) th item of data. Group 1: 1, 3, 4, 7, 8Group 2: 12, 13, 16, 17, 20 1, 3, 4, 7, 8 5 data items so the median is the 3rd item i.e 4 So the lower quartile is 4 LQ = 4 andUQ = 16

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Finding the Upper and Lower Quartiles for itemised data Case2 – an odd number of data items Split the data up into a lower and upper half and find the median of each half. Ex. Marks out of 20 for a test are: 1, 3, 4, 7, 12, 13, 16, 17, 20 9 marks so the Median = (n + 1) th item of data i.e the 5 th item which is 12 Delete this number 1, 3, 4, 7, 13, 16, 17, 20 as the 12 has been removed 8 marks so split into two groups of 4

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Group 2: 13, 16, 17, 20Group 1: 1, 3, 4, 7 13, 16, 17, 20 4 data items so the median is the 2 th item i.e 16 So the upper quartile is 16 The median of each group can be found using Median = (n + 1) th item of data. 1, 3, 4, 7 4 data items so the median is the 2 th item i.e 3 So the lower quartile is 3 LQ = 3 andUQ = 16

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