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Answer: Choice D</h3>
The five number summary is
- Min = 23
- Q1 = 26
- Median = 28.5
- Q3 = 30.5
- Max = 37
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Further Explanation:
The original data set is {24, 32, 25, 27, 37, 29, 30, 30, 28, 31, 27, 23}
It sorts to {23, 24, 25, 27, 27, 28, 29, 30, 30, 31, 32, 37} when going from smallest to largest.
There are n = 12 items in this set. The median is found between slots 6 and 7 because n/2 = 12/2 = 6
Circle the items in slot 6 and slot 7 to highlight 28 and 29 in that order. The midpoint is (28+29)/2 = 57/2 = 28.5 which is the median.
Median = 28.5
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Now break the set up into two pieces
L = {23, 24, 25, 27, 27, 28}
U = {29, 30, 30, 31, 32, 37}
L is the lower set below the median, U is the upper set above the median
The midpoint of L is (25+27)/2 = 26 and the midpoint of set U is (30+31)/2 = 30.5
This gives us Q1 = 26 and Q3 = 30.5 respectively
Q1 = first quartile
Q3 = third quartile
The min and max are simply the smallest and largest items of the set
min = 23
max = 37
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We have this five number summary:
- Min = 23
- Q1 = 26
- Median = 28.5
- Q3 = 30.5
- Max = 37
These five items directly determine the positioning of the box and whiskers. No extra info is needed.
The min and max handle the tips of the left and right whiskers if we don't have any outliers. In this case, we don't have outliers so we can ignore this aspect.
The Q1 and Q3 handle the left and right edges of the box
The median (aka Q2) is the vertical line inside the box. It doesn't have to be at the center of the box. It's simply anywhere inside.
With all this in mind, the best match is <u>choice D</u>
- The tip of the left whisker is at 23
- The left edge of the box is at 26
- The vertical line inside the box is at 28.5
- The right edge of the box is at 30.5
- The tip of the right whisker is at 37
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In other words, we can eliminate the following
- A) Because the right edge of the box for choice A is at 31 when it should be at 30.5
- B) The tip of the right whisker is at 35 when it should be at 37
- C) The tip of the left whisker is at 21 when it should be at 23
Since A, B, and C are eliminated, the only thing left is <u>choice D</u> which matches all aspects of the five number summary above.
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