Question

By how many units is the interquartile range for Orlando's data set greater than the interquartile range for Victor's data set? Victor's Data Set: {22, 29, 32, 27, 30} Orlando's Data Set: {36, 25, 33, 27, 35}

Answer 1

By 3 units is the interquartile range for Orlando's data set greater than the interquartile range for Victor's data set.

Explanation:

Given:

Victor's Data Set: {22, 29, 32, 27, 30}.

Orlando's Data Set: {36, 25, 33, 27, 35}.

Now, to find the units is the interquartile range for Orlando's data set greater than the interquartile range for Victor's data set.

So, we get the interquartile range of Victor's Data Set:

{22,27,29,30,32}

Q3 =
`(30+32)/(2)`

Q3 =
`(62)/(2) =31.`

Q1 =
`(22+27)/(2)`

Q1 =
`(49)/(2)=24.5`

Thus, interquartile range is:

Interquartile range =
`Q3-Q1`

Interquartile range =
`31-24.5=6.5`

The interquartile range of Victor's Data Set = 6.5.

Now, to get the interquartile range of Orlando's Data Set:

{25,27,33,35,36}

Q1 =
`(25+27)/(2)=(52)/(2) =26.`

Q3 =
`(35+36)/(2) =(71)/(2)=35.5.`

Thus, interquartile range is:

Interquartile range =
`Q3-Q1`

Interquartile range =
`35.5-26=9.5`

The interquartile range of Orlando's Data set = 9.5.

Now, to get the units of the interquartile range for Orlando's data set greater than the interquartile range for Victor's data set we subtract Victor's interquartile range from Orlando's interquartile range:

`The\ interquartile\ range\ of\ Orlando's\ Data\ Set\ -\ The\ interquartile\ range\ of\ Victor's\ Data\ Set`

`=9.5-6.5=3.`

Therefore, by 3 units is the interquartile range for Orlando's data set greater than the interquartile range for Victor's data set.