The sum of the squares of 65 observations equals 862. The sum of the observations equals 93. The sample standard deviation of the observations equals
________.
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A. B. C. D.C
For N observations, it is easy to show that
sample variance*(N-1) = (sum of squares) - N*(mean^2)
Hence, in this case, sample variance = (862 - 65*(93/65)^2)/64 = 11.39. The standard deviation then equals sqrt(11.39) = 3.37
Note: You should be careful about the difference between population variance and sample variance. The formula for population variance is: population variance*N = (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.