Answer: D) 3
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Explanation:
Original set = {29, 30, 28, 32, 28, 31, 27}
The set sorts to {27, 28, 28, 29, 30, 31, 32}
We can see that 29 is at the exact middle since {27,28,28} are the items below it, and {30, 31, 32} are the items above it.
Or we could note that there are 7 items in this set, so the middle will be at slot 7/2 = 3.5 which rounds up to 4, meaning the median is in slot 4
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Split the sorted set into two smaller sets
Let L = {27,28,28} be the set of items lower than the median
Let U = {30, 31, 32} be the upper items above the median
For set L, the middle is 28. This is the value of Q1, so Q1 = 28
For set U, we have Q3 = 31 as it's the middle of set U.
Subtracting Q3 and Q1 gets us the interquartile range (IQR)
IQR = Q3 - Q1
IQR = 31 - 28
IQR = 3
which points to choice D as the answer.
