Let's evaluate each of the given statements:

1. The sum of the deviations from each value in a data set to the mean, is always zero: This statement is true. When you sum the differences between each data point and the mean of the data set, the result is always zero. This is a property of the mean.

2. The sum of the squared deviations from the mean is always zero: This statement is false. The sum of the squared deviations from the mean is the variance, which is not zero unless all the data points are the same.

3. The standard deviation is in squared units: This statement is false. The variance is in squared units, but the standard deviation is in the same units as the original data because it is the square root of the variance.

4. The standard deviation is always greater than the variance: This statement is false. The standard deviation is the square root of the variance, so it is less than or equal to the variance. The only time the standard deviation and variance are equal is when they are both zero (which happens when all data points are the same).

So, the correct answer is: "The sum of the deviations from each value in a data set to the mean, is always zero."

Question

Let's evaluate each of the given statements:

1. The sum of the deviations from each value in a data set to the mean, is always zero: This statement is true. When you sum the differences between each data point and the mean of the data set, the result is always zero. This is a property of the mean.

2. The sum of the squared deviations from the mean is always zero: This statement is false. The sum of the squared deviations from the mean is the variance, which is not zero unless all the data points are the same.

3. The standard deviation is in squared units: This statement is false. The variance is in squared units, but the standard deviation is in the same units as the original data because it is the square root of the variance.

4. The standard deviation is always greater than the variance: This statement is false. The standard deviation is the square root of the variance, so it is less than or equal to the variance. The only time the standard deviation and variance are equal is when they are both zero (which happens when all data points are the same).

So, the correct answer is: "The sum of the deviations from each value in a data set to the mean, is always zero."

Knowee AI · Accepted Answer

Let's evaluate each of the given statements:

1. The sum of the deviations from each value in a data set to the mean, is always zero: This statement is true. When you sum the differences between each data point and the mean of the data set, the result is always zero. This is a property of the mean.

2. The sum of the squared deviations from the mean is always zero: This statement is false. The sum of the squared deviations from the mean is the variance, which is not zero unless all the data points are the same.

3. The standard deviation is in squared units: This statement is false. The variance is in squared units, but the standard deviation is in the same units as the original data because it is the square root of the variance.

4. The standard deviation is always greater than the variance: This statement is false. The standard deviation is the square root of the variance, so it is less than or equal to the variance. The only time the standard deviation and variance are equal is when they are both zero (which happens when all data points are the same).

So, the correct answer is: "The sum of the deviations from each value in a data set to the mean, is always zero."

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