Question

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

Answer 1

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

Explanation:

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`