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The following are the ages of 14 physics teachers in a school district.

28, 31, 35, 35, 40, 41, 47, 47, 48, 49, 50, 51, 53, 54

Notice that the ages are ordered from least to greatest.

Give the interquartile range for the data set.

Verified Answer :

Answer:  15

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Explanation

n = 14 items are in the set.

n/2 = 14/2 = 7 which means we'll look at the values in slots 7 and 8, which are the two "47"s. The midpoint of those items is 47.

The median is 47.

Another way to determine the median is to repeatedly cross off the first and last items until you narrow things down to the middle-most value. Once again the two "47"s are tied for the middle-most position, which is why we take the midpoint. This midpoint trick only applies when the sample size n is even.

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We have the median (47). What do we do with it? We'll use it to split the data into two halves such that:

  • L = set of stuff smaller than the median (also includes the median itself)
  • U = set of stuff larger than the median (also includes the median)

In this case,

  • L = {28, 31, 35, 35, 40, 41, 47}
  • U = {47, 48, 49, 50, 51, 53, 54}

Carefully note that each subset L and U has 7 values each.

The medians of sets L and U are 35 and 50 in that order.

Q1 = first quartile = median of set L = 35

Q3 = third quartile = median of set U = 50

IQR = interquartile range

IQR = Q3 - Q1

IQR = 50 - 35

IQR = 15

Side note: The IQR is one way to measure how spread out the data is. On a box-and-whisker plot, the IQR is the width of the box.

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