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

so the mean = 420/5 = 84

which you say is also the median, that is the middle number
Thus the sum of the 4 non-median numbers is 420 - 84 or 336

To find the sum of the 4 scores that are not the median, we first need to determine the average and the median of the 5 scores.

Let's assign variables to the scores: A, B, C, D, and E. Since the sum of the 5 scores is given as 420, we can write the equation:

A + B + C + D + E = 420 .............(1)

The average of the 5 scores is also the sum divided by the total number of scores, which in this case is 5:

(A + B + C + D + E)/5 = (A + B + C + D + E)/5 .............(2)

Next, we know that the average and the median have the same value. In a set of 5 numbers, the median is the middle value when the numbers are arranged in ascending order.

To start, let's assume that A ≤ B ≤ C ≤ D ≤ E. Since the median is the middle value, it must be C.

So, we have the following equation:

C = (A + B + C + D + E)/5 .............(3)

Now, using equations (2) and (3), we can write:

(A + B + C + D + E)/5 = C

Multiplying both sides of the equation by 5 gives:

A + B + C + D + E = 5C

Substituting equation (1) in place of the left side of the equation:

420 = 5C

Dividing both sides of the equation by 5 gives:

C = 84

So now we know that the median value is 84. To find the sum of the 4 scores that are not the median, we need to exclude C (the median) from the sum of the 5 scores.

The sum of the four scores (excluding C) is:

(A + B + D + E) = (420 - C) = (420 - 84) = 336

Therefore, the sum of the four scores that are not the median is 336.