Question

Micheal's mean score for five tests was 82. if four of those tests were 83,75,93, and 67, what was the fifth score on his test?

Answer 1

Let T represent the fifth test score. The average is the sum of scores divided by their number.

... 82 = (83 +75 +93 +67 +T)/5

... 410 = 318 +T . . . . . . . multiply by 5

... 92 = T . . . . . . . . . . . . subtract 318

The fifth score was 92.

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One of the ways I like to work problems like these is to add the differences from the mean. Those are ...

1, -7, 11, -15

so their sum is -10.

The final score must be 10 above the mean in order for this total to be zero. 10 above the mean is 92.