What is the standard deviation of {1, 1, 1, 3, 3, 3}?
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"Suppose that I don't have a formula for #g(x)# but I know that #g(1)
= 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Dec 13, 2015
Standard deviation (population):
Explanation:
The mean is clearly
Each value deviates from the mean by
So the square of each value's deviation from the mean is
and the average of the squared deviations (i.e. the variance,
Therefore the standard deviation (assuming the data represents the entire population) is
