Question

Which of the following is true of the data set represented by the box plot?

box plot with min at 10.5, Q1 at 11.5, median at 12.5, Q3 at 13.5, max at 15

The data contains at least one outlier.
The mean and median are most likely the same or very close.
The data is skewed to the right.
The median is 11.

Answer 1

the median is 11 so therefore the answer is the last one

Answer 2

The statement which is true about the box plot is:

• The mean and median are most likely the same or very close.

Explanation:

The box plot is given by:

Minimum value= 10.5

First quartile or lower quartile i.e.
`Q_1` = 11.5

Median or middle quartile or second quartile i.e.
`Q_2` = 12.5

Third quartile or upper quartile i.e.
`Q_3` = 13.5

and Maximum value = 15

• As we know that in a box plot the outlier lie out of the whisker that is the point is defined differently.

Hence, there are no outliers as none of the point is defined outside the whisker.

• Also, the left and right side of the box to the median is equal i.e. 1 units

( Since 12.5-11.5=1

and 13.5-12.5=1 )

Hence, the data is not skewed to the right.

• Also, the mean is calculated as follows:

`Mean=(10.5+11.5+12.5+13.5+15)/(5)\\\\\\Mean=(63)/(5)\\\\\\Mean=12.6`

Hence, the mean is close to Median

( since, Median= 12.5

and Mean=12.6)