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

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##