What was the standard deviation of Company R’s earnings per month for last year?
(1) The standard deviation of Company R’s earnings per month in the first half of last year was $2.3 million. (2) The standard deviation of Company R’s earnings per month in the second half of last year was $3.9 million.
I think in your answer explanation, you should make clear exactly what is necessary to compute standard deviation: the value of each of the specific terms in the set and the average of those terms. If you apply statements 1 and 2 together, you see that you do have the average of all 12 months: ((2.3M x 6) + (3.9M x 6))12 which equals 3.1M. But because you don\'t know what the values of the specific terms in the set are, you can not calculate stand devn for the entire year. Please let me know if don't agree.
your error rests in your notion of standard deviation. When you are multiplying 2.3 million by 6 what you are really doing is adding up the sum of the spaces between each value, you are not finding the average. For example, if i have a standard deviation of 5 for the following set
1, 6, 11, 16
The standard deviation is clearly 5 and the mean is clearly 11
What you did was multiply 5 x 4 = 20 and assumed the latter to be the mean. The product of the standard deviation and the number of data points does not yield the arithmetic mean of the set.
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