Question

9, 11, 10, 13, 8, 9, 11, 9

Compute the estimated population (sample) varianceand the estimated population standard deviation for the sample above  

Estimated pop. variance :

Estimated pop. standard deviation :

Why are the numbers computed here larger than Range: 5 μ: 10 Variance (σ²): 2.57 Standard deviation (σ): 1.60

Why must the estimates be computed this way?

Answer 1

estimated population variance is 2.5 714

estimated population standard deviation is 1.60 36

computed estimate population variance and standard deviation are less than given actual population variance and standard deviation because

actual variance=[( n-1)/n] X estimated variance

hence actual variance is less than estimated variance.

we use to calculate estimated variance in this way because above used formula is unbiased estimate of population variance.

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