To solve this problem, we need to understand the relationship between the average, median, and the individual scores.
Let’s denote the five distinct scores as S1, S2, S3, S4, S5. For simplicity, we can assume that the scores are arranged in ascending order, meaning:
- S1 < S2 < S3 < S4 < S5
Given that the sum of these five scores is 420:
S1 + S2 + S3 + S4 + S5 = 420
The average of these five scores can be calculated as follows:
Average =
( S1 + S2 + S3 + S4 + S5 ) / 5 = 420 / 5 = 84.
According to the problem, this average is the same as the median of the scores. In a set of five numbers, the median is the middle number when they are arranged in order. Thus:
Median = S3 = 84.
Now we can express the sum of the four scores that are not the median (i.e., S1, S2, S4, and S5) as:
Sum of four scores = S1 + S2 + S4 + S5
We already know the total sum of the five scores is 420:
Sum of four scores = S1 + S2 + S4 + S5 = 420 – S3
Substituting the value of S3 (which we found to be 84) gives:
Sum of four scores = 420 – 84 = 336.
Therefore, the sum of the 4 scores that are not the median is 336.