In a sample of n = 3 scores,if two scores are each below the mean by 2 points,then the third score is above the mean by 4 points.

Question

Quizplus · Accepted Answer

Let's assume the mean of the three scores is x.

If two scores are each below the mean by 2 points, their sum is (x-2)+(x-2)= 2x-4.

We know that the third score is above the mean by 4 points, so its value is x+4.

The sum of all three scores must equal 3x.

Therefore,

2x-4 + 2x-4 + x+4 = 3x

5x-4 = 3x

x = 2

This means that the mean of the three scores is 2.

If two scores are below the mean by 2 points, then they are both equal to 0.

The third score must be above the mean by 4 points, so it must be 6.

The three scores are 0, 0, and 6.

Therefore, the statement is true.

In a Sample of N = 3 Scores,if Two Scores