Short Essay on Arithmetic Mean !
The arithmetic mean,’ mean or average is calculated by summing all the individual observations or items of a sample and dividing this sum by the number of items in the sample. For example, as the result of a gas analysis in a respirometer an investigator obtains the following four readings of oxygen percentages:
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14.9
10.8
12.3
23.3
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___________
Sum=61.3
He calculates the mean oxygen percentage as the sum of the four items divided by the number of items—here, by four. Thus the average oxygen percentage is
Mean = 61.3 / 4 =15.325%
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Calculating a mean presents us with the opportunity for learning statistical symbolism. An individual observation is symbolized by Yi, which stands for the ith observation in the sample. Four observations could be written symbolically as Yi, Y2, Y3, Y4.
We shall define n, the sample size, as the number of items in a sample. In this particular instance, the sample size n is 4. Thus, in a large sample, we can symbolize the array from the first to the nth item as follows: Y1, Y2…, Yn. When we wish to sum items, we use the following notation:
The capital Greek sigma, ?, simply means the sum of items indicated. The i = 1 means that the items should be summed, starting with the first one, and ending with the nth one as indicated by the i = n above the ?. The subscript and superscript are necessary to indicate how many items should be summed. Below are seen increasing simplifications of the complete notation shown at the extreme left:
