The average of 5 distinct scores has the same value as the median of the 5 scores. The sum of the 5 scores is 420. What is the sum of the 4 scores that are not the median?

To solve this problem, we begin with the information provided:

• The sum of the 5 distinct scores is 420.
• The average of these scores equals the median.

First, we can find the average of the five scores. The average is calculated as the total sum divided by the number of scores:

Average = Total Sum / Number of Scores

Average = 420 / 5 = 84

Since we are told that the average equals the median, this means the median score is also 84.

Now, consider that the five scores must be distinct and arranged in ascending order. Let’s denote the scores as:

A, B, C (median), D, E

Here, C (the median) is 84. Consequently, we need to set up some equations based on the sum:

A + B + C + D + E = 420

Substituting C with 84:

A + B + 84 + D + E = 420

This simplifies to:

A + B + D + E = 420 – 84 = 336

We are asked to find the sum of the 4 scores that are not the median (A, B, D, and E). From our calculations above, we already know that:

The sum of the 4 scores that are not the median is 336.

So, the final answer is:

336