Which data set can you add to the data shown to increase the median of the data? 5 13 11 14 7 a.{2, 19} b.{6, 12, 16} c.{6, 11, 15} d.{3, 4, 14}

The median is the middle number in a set of data, or the arithmetic mean of two middle numbers if there is even number of elements in the set.

Sort the numbers from least to greatest:
5, 7, 11, 13, 14
The median is 11.

A. If you add {2, 19}:
2, 5, 7, 11, 13, 14, 19
The median is 11.

B. If you add {6, 12, 16}:
5, 6, 7, 11, 12, 13, 14, 16
The median is the mean of 11 and 12.
(11+12)/2=23/2=11.5
The median is 11.5.

C. If you add {6, 11, 15}:
5, 6, 7, 11, 11, 13, 14, 15
The median is the mean of 11 and 11.
(11+11)/2=22/2=11
The median is 11.

D. If you add {3, 4, 14}:
3, 4, 5, 7, 11, 13, 14, 14
The median is the mean of 7 and 11.
(7+11)/2=18/2=9
The median is 9.

In A and C the median of the new data is the same as the original median, in D it's less than the original median, only in B it's greater.
You can add {6, 12, 16} to the data to increase the median.
The answer is B.