Question

$10,9,15,27,14$

The number $15$ is to be added to the list above. Which of the following must be true about the median of the list?

• A. It will decrease from $15$ to $14$
• B. It will not change
• C. It will increase from $14$ to $15$
• D. It will increase from $14$ to $14.5$

Answer 1

The correct option is D It will increase from $14$ to $14.5$

To determine the median of a list, we first sort the list in numerical order, and then take the number in the middle.

The original sorted list is $9,10,14,15$, and $27$, so the median is originally $14$. If we add the number $15$ to the list, the new sorted list is $9,10,14,15,15$, and $27$.

The median of the new list is now $(14+15)/2=14.5$ (remember when there is no number in the middle, you take the average of the two numbers on either side of the middle).

So, the median has increased from $14$ to $14.5$.

Answer $D$ is the correct one.