Question

Select all of the true statements about the standard deviation of a quantitative variable. The standard deviation of a set of values is equal to 0 if and only if all of the values are the same. The standard deviation of a group of values is a measure of how far the values are from the mean. Standard deviation is resistive to unusual values. Changing the units of a set of values (e.g., converting from inches to feet) does not affect its standard deviation. If a set of values has a mean of 0 and a standard deviation that is not 0, then removing a data point with a value of 0 will have no effect on the standard deviation. Standard deviation is never negative.

Answer 1

Answer:

The standard deviation of a set of values is equal to 0 if and only if all of the values are the same; The standard deviation of a group of values is a measure of how far the values are from the mean; Standard deviation is never negative.

Step-by-step explanation:

Standard deviation is the distance, on average, that each point is from the mean.  The only way this value can be zero is if every value is the same as the mean, making all of the data values the same.

Since standard deviation is the square root of the variance, standard deviation is never negative.

Since the standard deviation is a measure of spread from the mean, which is not resistant to outliers, the standard deviation itself is not resistant to outliers.

Changing the units of a set of values involves multiplying by a constant.  For example, changing from feet to inches involves multiplying each data value by 12.  When we do this, the standard deviation will also be multiplied by the same constant.

For a set of values with mean of 0 and a standard deviation that is not 0, removing a data point with a value of 0 will have an effect on the standard deviation.  For example, the data set 3, 2, 1, 0, -1, -2 -3 has a mean of 0.  The standard deviation of the set is 2.  Removing the data point 0 increases the standard deviation to about 2.2.