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?

Solution:

Given, the average of 5 distinct scores is equal to the median of the 5 scores.

Sum of 5 scores = 420.

Average = total sum of all the numbers / Number of items in the set

Average = 420 / 5

Average = 84

Median depends only on one or two middle most values. 

When the number of observations is odd, the median depends on the middle most value given by the value corresponding to (n+1)/2 term.

Incase of even numbers, it depends on the average of two middle values given by (n+1)/2 and (n+2)/2 terms.

Now, median = average (given)

Median = 84

The sum of 4 scores that are not the median = total sum of 5 scores - median of 5 scores

Sum of 4 scores = 420 - 84

= 336

Therefore, the sum of 4 scores except median is 336.

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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?

Summary:

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