What is the interquartile range of 86, 72, 85, 89, 86, 92, 73, 71, 91, 82?

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What is the interquartile range of 86, 72, 85, 89, 86, 92, 73, 71, 91, 82?

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Answer 1 · 2017-05-29T18:25:03

$I Q R = 16$ $IQR=16$

Explanation:

$arrange the data set in ascending order$ $"arrange the data set in ascending order"$

$71 x 72 x 73 x 82 x 85 ↑ x 86 x 86 x 89 x 91 x 92$ $71color(white)(x)72color(white)(x)color(magenta)(73)color(white)(x)82color(white)(x)85color(red)(uarr)color(white)(x)86color(white)(x)86color(white)(x)color(magenta)(89)color(white)(x)91color(white)(x)92$

$the quartiles split the data into 4 groups$ $"the quartiles split the data into 4 groups"$

$the median Q_{2} = \frac{85 + 86}{2} = 85.5$ $"the median "color(red)(Q_2)=(85+86)/2=85.5$

$the lower quartile Q_{1} = 73$ $"the lower quartile "color(magenta)(Q_1)=color(magenta)(73)$

$the upper quartile Q_{3} = 89$ $"the upper quartile "color(magenta)(Q_3)=color(magenta)(89)$

$the interquartile range (I Q R) = Q_{3} - Q_{1}$ $"the interquartile range " (IQR)=Q_3-Q_1$

$t h e \int e r q u a r t i \leq r a n \geq \times \times x = 89 - 73$ $color(white)(the interquartile rangexxxxx)=89-73$
$t h e \int e r q u a r t i \leq r a n \geq \times \times x = 16$ $color(white)(the interquartile rangexxxxx)=16$

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What is the interquartile range of 86, 72, 85, 89, 86, 92, 73, 71, 91, 82?

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