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Answer: Choice C</h3>
min = 20
Q1 = 24
median = 27
Q3 = 31
max = 34
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Explanation:
Original Data Set = {29, 31, 27, 20, 25, 34, 24}
Sorted Data Set = {20, 24, 25, 27, 29, 31, 34}
The middle-most value of the sorted set is 27, since there are 3 values above it and 3 values below. So the median is 27.
The median is represented by the vertical line inside the box. It does not have to be at the visual midpoint between the left and right edges. It simply needs to be anywhere inside the box.
So we can rule out choice B for instance because this answer choice shows a median of 25, when we want 27 instead.
Choices A, C and D all have the same median of 27.
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Break up the sorted set into two smaller sets like this
L = {20, 24, 25}
U = {29, 31, 34}
L represents the set of lower values, which are smaller than the median. U is the upper set of values larger than the median. The median itself is not in L or U.
Find the median of L and U to get 24 and 31 respectively. These are the Q1 and Q3 values in that order.
Q1 = 24
Q3 = 31
These are the left and right edges of the box.
We can cross choice A off the list because the right edge of the box in that diagram is at 29 instead of 31.
The answer is between C and D.
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The last things to consider are the min and max, which are the smallest and largest elements. These are the left and right tips of the whiskers, assuming that we don't have small or large outliers. In this case, we don't have to worry about outliers.
The min and max is 20 and 34 which must mean the answer is choice C
We can rule out choice D because the max shown here is 35.
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In short, the data set has the following five number summary:
- min = 20
- Q1 = 24
- median = 27
- Q3 = 31
- max = 34
all of these five values correspond to a specific visual feature of the boxplot (see diagram below)
