How do you find the range and interquartile range for 37, 19, 13, 11, 10?

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Answer 1 · 2017-01-20T07:29:17

Range is $27$ and interquartile range is $17 1/2$ .

Let us first arrange them in increasing order and data appears as

$10,11,13,19,37$

As the range is difference between maximum and nimimum

Range is $37-10=27$

Median is the value of $((n+1)/2)^(th)$ term i.e. $(5+1)/2=3^(rd)$ term i.e. $13$

First quartile $Q_1$ is $((n+1)/4)^(th)=(1 1/2)^(th)$ term and third quartile $Q_3$ is $3((n+1)/4)^(th)=(4 1/2)^(th)$ term.

Hence, we can take $Q_1$ as $(10+11)/2=10 1/2$ and $Q_3$ as $(19+37)/2=28$ .

As interquartile range is $Q_3-Q_1$ , it is $28-10 1/2=17 1/2$