The sum of the squares of 1,200 observations equals 9,830. The sum of the observations equals 1,510. The population standard deviation of the observations equals ________.
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A. B. C. D.B
For N observations, it is easy to show that
population variance*N = (sum of squares) - N*(mean^2)
The mean equals 1,510/1,200 = 1.258. Hence, population variance = (9,830 - 1,200*1.258^2 )/1,200= 6.608. The standard deviation then equals sqrt(6.608) =
2.57
Note: You should be careful about the difference between population variance and sample variance. The formula for sample variance is: sample variance*(N-1) = (sum of squares) - N*(mean^2)
You can expect an exam question which asks for population variance, with the choices given containing both the population and the sample variances or vice versa.