Question 1155289: Mrs. Gitterman gave a quiz to each of her three classes. Each of her classes has 12 students. When she found the mean for each class, she was surprised to see that the mean for each class was 80%. However looking at the individual scores, she found that the distribution of scores in each class looked very different. Write three sample sets of data that have different distributions of quiz scores but have class means of 80%
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! number of elements is 12.
the mean is the sum divided by the number of elements.
if the sum is the same, then the mean is the same.
sample 1 - everybody got 80.
sum is 12 * 80 = 960
mean is 960 / 12 = 80%
sample 2 - 6 got 70 and 6 got 90
sum is 6 * 70 + 6 * 90 = 410 + 540 = 960
mean is 960 / 12 = 80%
sample 3 - 3 got 60, 4 got 100, 1 got 40, 2 got 90, 1 got 75, 1 got 85
sum is 3 * 60 + 4 * 100 + 40 + 2 * 90 + 75 + 85 = 960
mean is 960 / 12 = 80%
as long as the sum of all 12 elements is 960, the mean will be 80.
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