Which box plot represents the data? 30, 35, 25, 5, 5, 25, 40, 45, 50, 10, 15, 40

The answer is choice A



Explanation:

The original list is
A = {30, 35, 25, 5, 5, 25, 40, 45, 50, 10, 15, 40} 

The sorted list is 
B = {5, 5, 10, 15, 25, 25, 30, 35, 40, 40, 45, 50}

The middle most value is a tie between 25 and 30. The midpoint is 27.5 (add up those values, then divide by 2). So the median is 27.5

Only choice A has the median being 27.5, which is the vertical bar inside the boxplot (aka box and whisker plot). So we can stop here if you want.

To find the value of Q1, look at the values smaller than the median which is this set 
L = {5, 5, 10, 15, 25, 25}
L for lower set of values smaller than the median

The median of set L is (10+15)/2 = 25/2 = 12.5; it is the midpoint of 10 and 15 as they are tied for the middlemost value. So the value of Q1 is 12.5. Choice A reflects this as the proper value of Q1

The upper set of values U is
U = {30, 35, 40, 40, 45, 50}
which has a median of (40+40)/2 = 80/2 = 40
The value of Q3 is 40

The value Q1 represents the left edge of the box
The value Q3 represents the right edge of the box.

The min = 5 and the max = 50 which are the smallest and largest values in the set

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