<h3>
Answer: Choice B</h3>
Q1 = 7, Q2 = 10, Q3 = 13.5
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Explanation:
Start with {5,7,7,8,10,11,12,15,17}
Notice how this data set is already sorted for us from smallest to largest.
Cross off the first and last items to get {7,7,8,10,11,12,15}
Repeat the last step to get this smaller set {7,8,10,11,12}
Repeat again: {8,10,11}
Repeat one more time: {10}
The 10 is at the very center, so it is the median aka the value of Q2.
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An alternative way to get the median is to follow these steps:
There are n = 9 numbers in the original set before we crossed off any items. The middle number is in slot 5 because n/2 = 9/2 = 4.5 rounds up to 5. The value in the fifth slot is 10, so 10 is the median.
There are 4 items below the median and 4 items above it, giving n = 4+1+4 = 9 items total.
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Next, break the data set into two smaller groups
L = lower set = every value below the median
L = {5, 7, 7, 8}
U = upper set = every value above the median
U = {11, 12, 15, 17}
The median itself is in neither set L nor set U.
The median of set L is (7+7)/2 = 7, so this is the value of Q1
The median of set U is (12+15)/2 = 13.5 which is the value of Q3
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Summary:
Q1 = 7
Q2 = 10 (aka the median of the original set)
Q3 = 13.5
