Joe is given five tests, each with a maximum score of 100 points. The mean of his test scores is 90. If all his tests have different grades and all the grades are whole numbers, what is the lowest grade he could have scored?

We know that he took 5 tests, mean is equal 90 so we know that following equations will be true if x will be sum of 5 scores: 5 x ​ = 90 x = 450 Also we have to remember that max points that he could get is 100 so to find the lowest score he could get we have to do equation like this 2 100 + y ​ = 90 100 + y = 180 y = 80

Answered by Scryt | 2024-06-10

If the Mean = 90 for 5 test values it means that there was a variation of values between maximum i-e 100 and minimum that may be any number not known. The possible minimum value is when 4 tests result in 100 and the 5th is unknown it means Mean = [(4X 100)+x] / 5 * 90 = (400+x) / 5*
400 + x = 90 X 5 * x = 450 -400 = 50*
So the minimum possible test result is 50.

Answered by littlestar | 2024-06-10

Joe's lowest possible score, given that he has five tests with a mean score of 90 and all tests have different whole number grades, is 56. This is calculated by maximizing the other four scores to 100, 99, 98, and 97. Thus, the sum of these four scores and the required total leads to the conclusion that he could have scored 56 on his lowest test.
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Answered by Scryt | 2024-12-20