Given are the eight values, [10, 9, 5, 18, 12, 13, 5, 20]. Which data value when added to the data set does not change the median? A. 5     B. 10    C. 11    D. 12

To answer this question, we first need to understand what the median is. The median is the middle value in a data set when the values are arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle values.

Step 1: Arrange the given values in ascending order: [5, 5, 9, 10, 12, 13, 18, 20]

Step 2: Since there are 8 values (an even number), the median is the average of the 4th and 5th values. So, the median of the given data set is (10 + 12) / 2 = 11.

Step 3: Now, we need to find which value when added to the data set does not change the median.

A. If we add 5, the new data set is [5, 5, 5, 9, 10, 12, 13, 18, 20]. The median is 10, which is different from the original median.

B. If we add 10, the new data set is [5, 5, 9, 10, 10, 12, 13, 18, 20]. The median is 10, which is different from the original median.

C. If we add 11, the new data set is [5, 5, 9, 10, 11, 12, 13, 18, 20]. The median is 11, which is the same as the original median.

D. If we add 12, the new data set is [5, 5, 9, 10, 12, 12, 13, 18, 20]. The median is 11, which is the same as the original median.

So, the answer is C. 11 and D. 12. Both these values when added to the data set do not change the median.