19. the median of a set of data containing 9 items was found. four data items were added to the set. two of…

19. 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? a. it is the average of the 2 new lower values. b. it is the same as the original median. c. it is the average of the 2 new higher values. d. it is greater than the original median. e. it is less than the original median.

19. 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? a. it is the average of the 2 new lower values. b. it is the same as the original median. c. it is the average of the 2 new higher values. d. it is greater than the original median. e. it is less than the original median.

Answer

Explanation:

Step1: Recall median concept

For a data - set with $n = 9$ (odd number of items), the median is the $\left(\frac{n + 1}{2}\right)$-th value when the data is arranged in ascending order. Here, the median is the 5 - th value.

Step2: Analyze new data - set

Four data items are added, two greater and two less than the original median. Now the number of data items is $n=9 + 4=13$ (still an odd number). When the data is arranged in ascending order, the position of the median is $\frac{13 + 1}{2}=7$-th value. The two new lower - value items are added before the original median, and the two new higher - value items are added after the original median. The relative position of the original median within the ordered data - set does not change in terms of it being the middle value among the original 9 values and the new values added symmetrically (two less and two greater). So the median of the new data - set is the same as the original median.

Answer:

B. It is the same as the original median.