Question

The box plots show the lengths of the songs on two digital music players in minutes. Lengths of Songs on Digital Music Players Music Player X Music Player Y 4 나 + + 4.5 + 5 + 7 3.5 4 5.5 6 6.5 7.5 Number of Minutes Which statement is best supported by the information in the box plots? F The interquartile range of the data for Music Player X is equal to the interquartile range of the data for Music Player Y. G The interquartile range of the data for Music Player X is greater than the interquartile range of the data for Music Player Y. H The median length of the songs on Music Player X is equal to the median length of the songs on Music Player Y. J The median length of the songs on Music Player X is less than the median length of the songs on Music Player Y.

Answer 1

From the box plot it follows:

For the music player X, the quartles are:

$Q_3=6.5,Q_1=4.5$

Hence the interquartile range for music player X is given by:

$(IQR)_x=Q_3-Q_1=6.5-4.5=2$

Similarly for the music player Y, the quartiles are

$Q_3=5,Q_1=4$

So the interquartile range for music player Y is given by:

$(IQR)_y=Q_3-Q_1=5-4=1$

Therefore it follows:

$(IQR)_x>(IQR)_y$

Therefore option G is correct.