Carefully review the formulas for the population standard deviation and the samp

Question

Carefully review the formulas for the population standard deviation and the sample standard deviation. Please note - the answer is not option D.

Descrbe the dtference between the calculation of population standard deviation and that of samole standard deiation. Let N be the number of data entries in a population and n be the number of data enties in a sample data set Choose the correct answer below O A. When cakculating the population standard devation, the sum of the squared deiation is dnided by the number of entnes, N-1, then the square root of the result is taken O B. When calculating the population standard deviation, the sum of the squared desiation is diided by N. then the square root of the result is taken. When calculating the sample c. When calculating the population standard deviation the sum of the square d nation is d i ed by N- When calculating the sample standard dewation the sum of the When calculating the sample standard deviation, the sum of the squared deviations is divided by n, then the square root of the result is taken standard devfation, the surn of the squared deviations is diided by n-1, then the square toot of the result is taken squared deviations is diwided by n deviations is dhided by niH1 D. When calculating the population standard deviation, the sum of the squared denation is diided by N When calculatimg the sample standard deviation the sum of the squared

Explanation / Answer

How ito calculate the standard deviation

1. Compute the square of the difference between each value and the sample mean.

2. Add those values up.

3. Divide the sum by n-1. This is called the variance.

4. Take the square root to obtain the Standard Deviation.

Why n-1?

Why divide by n-1 rather than n in the third step above? In step 1, you compute the difference between each value and the mean of those values. You don't know the true mean of the population; all you know is the mean of your sample. Except for the rare cases where the sample mean happens to equal the population mean, the data will be closer to the sample mean than it will be to the true population mean. So the value you compute in step 2 will probably be a bit smaller (and can't be larger) than what it would be if you used the true population mean in step 1. To make up for this, divide by n-1 rather than n.v This is called Bessel's correction.

B option

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