A sample of 16 observations has a standard deviation of 2. Which of the following is the sum of the squared deviations from the sample mean?Group of answer choices16.64.60.30.

The sum of the squared deviations from the sample mean is calculated by squaring the standard deviation and then multiplying it by the sample size.

Here are the steps to calculate it:

1. Square the standard deviation: 2^2 = 4
2. Multiply the squared standard deviation by the sample size: 4 * 16 = 64

So, the sum of the squared deviations from the sample mean is 64.

The correct answer is: 60.

Explanation:

1. The standard deviation is a measure of the amount of variation or dispersion in a set of values.

2. The formula for the standard deviation is the square root of the variance. The variance is calculated as the sum of the squared deviations from the mean divided by the number of observations minus 1.

3. In this case, we know the standard deviation (2) and the number of observations (16). We can square the standard deviation to get the variance (2^2 = 4).

4. To find the sum of the squared deviations from the mean, we multiply the variance by the number of observations (4 * 16 = 64).

5. However, because the standard deviation formula uses n-1 (degrees of freedom) instead of n in the denominator, we need to adjust our calculation. The correct calculation is 4 * 15 = 60.

6. Therefore, the sum of the squared deviations from the mean is 60.

The sum of the squared deviations from the sample mean is also known as the sum of squares. It can be calculated using the formula:

Sum of Squares = (n-1) * s^2

where n is the sample size and s is the standard deviation.

In this case, n = 16 and s = 2. Substituting these values into the formula gives:

Sum of Squares = (16-1) * 2^2 = 15 * 4 = 60

So, the sum of the squared deviations from the sample mean is 60. Therefore, the correct answer is 60.