The median of a set of data containing 9 items was found

The median of a set of data containing 9 items was found. Four data items were added to the set. Two of these items were greater than the original median, and the other 2 items were less than the original median. Which of the following statements must be true about the median of the new data set?

1. It is the average of the 2 new lower values.
2. It is the same as the original median.
3. It is the average of the 2 new higher values.
4. It is greater than the original median.
5. It is less than the original median. 

Answer

The correct answer is B.

The median is the middle value (fifth item in this case) when data is arranged in ascending or descending order.

When the additional 4 data items are put into the list, there are 9 + 4 = 13 items on the list. Because 2 of these items are greater than the original median and 2 of these items are less than the original median, the original median is the middle value in the new set. That makes the original median the new median.