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# Histograms

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https://vle.mathswatch.co.uk/images/questions/question2628.png   Feb 13, 2018
edited by qualitystreet  Feb 13, 2018

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median score=116

lower quartile=102

explanation:

The Median is simply the number in the exact middle, or the 7th number in the list =140

Find the 25th percentile of the list:
(80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200)

The 25th percentile of the ordered list (80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200) should be the median of the lower half of the list.
Since the list has an odd number of elements, we take the average of the medians of the two lists that are closest to being the lower half of the list:
(80, 90, 100, 110, 120, 130) and (80, 90, 100, 110, 120, 130, 140)

To find the median of the ordered list (80, 90, 100, 110, 120, 130), we must find the two elements in the middle of the list.
The two elements in the middle of the list (80, 90, 100, 110, 120, 130) are 100 and 110:
(80, 90, 100, 110, 120, 130)

The median is the average of the two elements in the middle of the sorted list.
The median is the average of the two middle elements, 100 and 110. This average is:
(100 + 110)/2 = 105

The median of the ordered list (80, 90, 100, 110, 120, 130, 140) is the element in the middle of the list.
The median of the list (80, 90, 100, 110, 120, 130, 140) is the element in the middle, which is:110

Now that we know that the median of {80, 90, 100, 110, 120, 130} is 105 and the median of {80, 90, 100, 110, 120, 130, 140} is 110, we have only to find the average of the two medians.
The 25th percentile is the average of 105 and 110. This average is:
(105 + 110)/2 = 215/2 =107.50   Feb 13, 2018
edited by lynx7  Feb 13, 2018