If the median of the distribution 4, 5, 9, 11, 14 is 9, what would the median be if 14 were replaced by 19?

• A. 9
• B. 10
• C. 11
• D. 12

Answer: (A)

To determine the median of the new distribution after replacing 14 with 19, we first need to understand the concept of the median. The median is the middle number in a sorted list of numbers. If there is an odd number of values, the median is the middle one; if there is an even number, it is the average of the two middle values.

Initially, the distribution is 4, 5, 9, 11, and 14. When arranged in ascending order, this remains the same since they are already in order: 4, 5, 9, 11, 14. The median, being the middle value, is the third number in this list, which is 9.

Now, when we replace 14 with 19, the new distribution becomes 4, 5, 9, 11, and 19. Sorting this new list still results in 4, 5, 9, 11, and 19. Again, since there are five numbers (an odd count), the median will still be the third number in this sorted list.

The third number remains 9. Therefore, despite the change in the last value of the distribution, the median does not