ave - N data = 10, so we bring that into the summation...

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Averages: A Simple Treatment 16th February 2010 Consider the following series of 10 ( N data = 10) numbers (we are being discrete : 10 , 30 , 20 , 80 , 80 , 70 , 70 , 60 , 50 , 30 What is the average of these discrete numbers? That is, what is the average value of x ? Average = 1 N data [(10) + (20) + (30 + 30) + (50) + (60) + (70 + 70) + (80 + 80)] Now, we can invoke the idea of a probability for each value we have to consider. This is the discrete analogue of the probability distribution function that we have considered as a continuous function.
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Unformatted text preview: N data = 10, so we bring that into the summation explicitly for each term. Average = (10) 1 10 + (20) 1 10 + (30) 2 10 + (50) 1 10 + (60) 1 10 + (70) 2 10 + (80) 2 10 If we consider the fractions that occur in the sum as probabilities for each discrete value of x , then the average is represented as: Average = N data X i =1 ( value ) i f (( value ) i ) In the continuous limit, we replace the summation by an integration. 1...
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