The sum of 16 reciprocals (1 over the number) is found to equal 4. What is the harmonic mean of the original (i.e., non-reciprocated) scores?

To find the harmonic mean of the original scores, we need to determine the arithmetic mean of the reciprocals of the original scores. In this case, we know that the sum of 16 reciprocals is equal to 4, so each reciprocal has a value of 4 divided by 16, which is 1/4.

Now, let x be the original score. The reciprocal of x is 1/x. We can set up the equation:

1/x + 1/x + 1/x + ... + 1/x (16 times) = 1/4

To find the harmonic mean, we need to find x. We multiply both sides of the equation by x:

16/x = 1/4

Now, cross-multiply:

4 * 16 = x

x = 64

Therefore, the harmonic mean of the original scores is 64.