Question

What are the possible values of the standard deviation, s, of a set of observations?

a. s can be any number, positive, 0, or negative
b. s can be 0 or positive, but not negative
c. s can be positive, but not 0 or negative
d. s can be negative
e. s must be between -1 and 1

Answer 1

b.

Step-by-step explanation:

standard deviation measures the degree of dispersion of a dataset relative to its mean and is calculated as the square root of the variance, which determines each data point's deviation relative to the mean.

in other words, for each data point is difference to the mean value is calculated and squared (so, this is always positive, no matter if the data point is larger or smaller than the mean). all these squared differences are added, and then the standard deviation is the positive square root of that sum.

it is the same, if all the data points are dispersed in the same way below the mean or above.

therefore, the standard deviation is always positive. in an extreme case it can be 0 (all data points have the same value), but it cannot be negative. it would not make any sense to use the negative square root in the calculation mentioned above.

therefore, b. is the right answer.

Answer 2

The standard deviation s can only be 0 or a positive number since it measures the spread of data values from the mean. It cannot be negative.

Step-by-step explanation:

The possible values of the standard deviation, s, of a set of observations are such that s can be 0 or positive, but not negative.

The standard deviation is a measure of how far data values are from their mean, which inherently cannot be a negative value.

When all data points are equivalent, exhibiting no variability, the standard deviation will be zero; otherwise, it will be a positive number that increases as the variability or spread in the data increases.

The standard deviation is denoted as s for sample standard deviation, and as Greek letter σ (sigma) for population standard deviation.