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How do you calculate an overall average from a set of component averages?
I recommend you do not try to average a set of components, because your result may be not be accurate. The best way to find an overall average is to average the entire data set.EXAMPLE: You have three columns of ten numbers each with an average listed at the bottom of each, say A11, B11, and C11. There are two ways you can solve this:Combine all the averages and divide by 3. [=SUM(A11:C11)/3] - But, the result may not reflect the average of the entire data set.Calbulate the average for all 30 numbers in the data set. [=SUM(A1:C10)/30] - This would give a much more accurate representation of the entire data set.
A bag contains 5 balls two balls are drawn at a random and found to be red what is the probability that all balls are red?
The probability that all balls are red is 0.50 or 50%.EXPLANATIONSuppose there are 4 boxes with 5 balls each.Box A has 2 red balls.Box B has 3 red balls.Box C has 4 red balls.Box D has 5 red balls.The probability of drawing at random 2 red balls for each box is:Box A; P(2 red balls) = (2/5)∙(1/4) = 2/20 = 1/10Box B; P(2 red balls) = (3/5)∙(2/4) = 6/20 = 3/10Box C; P(2 red balls) = (4/5)∙(3/4) = 12/20 = 6/10Box D; P(2 red balls) = (5/5)∙(4/4) = 20/20 = 10/10Now, suppose we do the drawing of 2 balls experiment 10 times on each boxgiving a total of 40 experiments. The probabilities calculated above are the"expected" results, that is; out of the 40 experiments (drawing of 2 balls), twored balls resulted:1 time came from box A3 times from box B6 times from box C10 times from box DNotice that from the 40 experiments, 20 result in 2 red balls.From here we have that when drawing 2 red balls the probability that it camefrom a box containing 2 red balls (box A), 3 red balls (box B), 4 red balls (box C)or 5 red balls is:P(A) = 1/20 = 0.05 = 5%P(B) = 3/20 = 0.15 = 15%P(C) = 6/20 = 0.30 = 30%P(D) = 10/20 = 0.50 = 50%
