Question

A gym teacher compares the points scored by three basketball teams in their last 11 games. The points scored by Team A are shown. The scores of Team B and Team C are shown by the following box plots. Select a box in each row of the table to compare the median scores and the interquartile range of scores for the three teams.

Answer 1

There are
`n=11` scores given.

`\text{Median}=(11+1)/(2) =6^{\text{th}} \ \text{term}=78`

`\text{Lower quartile range}=(11+1)/(4) =3^{\text{rd}} \ \text{term}=74`

`\text{Upper quartile range}=(3(11+1))/(4) =9^{\text{th}} \ \text{term}=88`

Interquartile range of team
`\text{A}=88-74=14`

By box and whisker plots,

Median of team
`\text{A}=78`

Median of team
`\text{B}=86`

Median of team
`\text{C}=82`

Team B has the highest median

`\bold{Interquartile \ range = upper \ quartile - lower \ quartile}`

Interquartile range of team
`\text{A}=14`

Interquartile range of team
`\text{B}=90-78=12`

Interquartile range of team
`\text{C}=86-70=16`

Therefore, Team B has the lowest interquartile range and the highest median.