What is the interquartile range for this set of data? 11, 19, 35, 42, 60, 72, 80, 85, 88

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Answer 1 · 2017-06-30T13:17:03

See a solution process below:

This data set is already sorted. So, first, we need to find the median:

$11, 19, 35, 42, 60, 72, 80, 85, 88$ $11, 19, 35, 42, color(red)(60), 72, 80, 85, 88$

Next we put parenthesis around the upper and lower half of the data set:

$(11, 19, 35, 42), 60, (72, 80, 85, 88)$ $(11, 19, 35, 42), color(red)(60), (72, 80, 85, 88)$

Next, we find Q1 and Q3, or in other words, the median of the upper half and lower half of the data set:

$(11, 19, ∣ 35, 42), 60, (72, 80, ∣ 85, 88)$ $(11, 19,color(red)(|) 35, 42), color(red)(60), (72, 80,color(red)(|) 85, 88)$

$Q 1 = \frac{35 + 19}{2} = \frac{54}{2} = 27$ $Q1 = (35 + 19)/2 = 54/2 = 27$

$Q 3 = \frac{80 + 85}{2} = \frac{165}{2} = 82.5$ $Q3 = (80 + 85)/2 = 165/2 = 82.5$

Now, we subtract $Q 1$ $Q1$ from $Q 3$ $Q3$ to find the interquartile range:

$82.5 - 27 = 55.5$ $82.5 - 27 = 55.5$