Question

Which of the following seven distances (in feet) in the triple jump.

29, 30, 28, 32, 28, 31, 27

What is the interquartile range of her distances?

Answer 1

Answer: D) 3

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Step-by-step 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.