Question

Find the interquartile range of {61,65,65,66,72,75,77,79,81,89,92,99}

Answer 1

Given:

61,65,65,66,72,75,77,79,81,89,92,99.

There are 12 number of data.

Dividing the set into quartiles, each quarter will have 3 terms as

`\mleft\lbrace61,65,65\mright\rbrace,\mleft\lbrace66,72,75\mright\rbrace,\mleft\lbrace77,79,81\mright\rbrace,\mleft\lbrace89,92,99\mright\rbrace.`

We need to find lower Quartile and upper Quartile to compute the interquartile range.

`Lower\text{ Quartile }(Q_1)=(65+66)/(2)=65.5`

`Upper\text{ Quartile }(Q_3)=(81+89)/(2)=85`

The formula interquartile range is

`interquartile\text{ }range=Q_3-Q_1`
`\text{ Substitute }Q_1=85\text{ and }Q_3=65.5\text{ in the formula, we get}`

`interquartile\text{ }range=85-65.5`

`interquartile\text{ }range=19.5`

Hence the interquartile range of the given set is 19.5.