Question 171205This question is from textbook
: the speeds in miles per hour of 30 cars were checked by radar, the data is as follows:
62 67 69 72 75 60 58 86 74 68
56 67 82 88 90 54 67 65 64 68
74 65 58 75 67 65 66 64 45 64
Find the upper and lower quartiles?
This question is from textbook
Answer by Mathtut(3670)   (Show Source):
You can put this solution on YOUR website! arrange in ascending order:
:
(45,54,58,58,60,62,64,64,64,65,65,65,66,67,67,67,67,68,68,69,72,74,74,75,75,82,84,86,88,90)
first we take the median value for this set..since it is positive you take the 15 and 16th terms and divide by two....just so happens the are equal so 67 is the median. Now we split these groups in half.
:
(45,54,58,58,60,62,64,64,64,65,65,65,66,67,67) and
:
(67,67,68,68,69,72,74,74,75,75,82,84,86,88,90)
:
now to find the lower quartile we find the median of the lower group
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since there is an odd number of 15 in the group, the middle is the 8th term which is 64. Therfore  is the lower quartile
:
the upper quartile is found in the upper group...again we are looking for the 8th term because there is an odd number of 15 in the group. 8th term is 74..so the upper quartile is 
some methods exclude the median when breaking the original group in two...I used the method that includes the median.
If you excluded the median you would end up with lower quartile still being 64 but the upper quartile would be 74+75/2=74.5
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