The box plots display the same data for the number of crackers in each snack bag, but one includes the outlier in the data and the other excludes it. 4, 14, 15, 15, 16, 16, 18, 19, 20, 20, 21 number of crackers in each bag, with outlier number of crackers in each bag, without outlier which statement comparing the box plots is true? both the median and the range changed. both the range and the lower quartile changed. both the median and the interquartile range changed. both the interquartile range and the lower quartile changed.

I took the test the answer is A "both the median and the range changed."

Both the median and the range changed.

Step-by-step explanation:

This data set is already in order:

4, 14, 15, 15, 16, 16, 18, 19, 20, 20, 21

The range is the difference between the minimum and maximum values.  This makes the range (with the outlier):

21 - 4 = 17

The median is the middle value; it is also known as Q2, the second quartile.  With the outlier, Q2 = 16.

The first quartile, Q1, is the middle of the lower half of data, below the median.  With the outlier, Q1 = 15.

The third quartile, Q3, is the middle of the upper half of data, above the median.  With the outlier, Q3 = 20.

The interquartile range, IQR, is the difference between Q3 and Q1.  With the outlier, IQR = 20 - 15 = 5.

Taking the outlier out, we have:

14, 15, 15, 16, 16, 18, 19, 20, 20, 21

The range is 21-14 = 7.  This is different.

The median is between 16 and 18; this makes it

(16+18)/2 = 34/2 = 17.  This is different.

Q2 is 15.  This is the same.

Q3 is 20. This is the same.

IQR is 5.  This is the same.

This means the only things that changed were the median and the range.