The following data represents the ages of different participants in a game show. Find the interquartile range of the data given below.

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Solution

The correct option is D 16

Since there are 10 values, the median $= \frac{24 + 25}{2} = \frac{49}{2} = 24.5$ years.
We divide the given data set into an upper half and a lower half.

There are 5 values in the lower half, so the lower quartile = middle value of the lower quartile
$Q_{1} = 16$
There are 5 values in the upper half, the upper quartile = middle value of the upper quartile
$Q_{3} = 32$

The interquartile range $= Q_{3} - Q_{1} = 32 - 16 = 16$

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