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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.
- 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
Standard deviation measures how spread a given data set.
For example, let's consider the following data set and corresponding standard deviation;
(a) data set A = 7, 7, 7, 7, 7,
(b) data set B = 2, 4, 6, 8, 10
(c) data set C = -10, -5, 0, 5, 10
In the given data set above, we can deduce the following;
- data set C has the highest standard deviation because the values in the data set are more spread out compared to others. The negative sign does not affect the standard deviation.
- data set A has the least standard standard deviation, because the data set are more clustered compared to others.
- For the data set A, mean = 7 and standard deviation = (7-7) + (7-7) + (7-7) + (7-7) + (7-7) = 0
Thus, we can conclude the following;
- 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
- Decreasing or increasing values in a data set affect standard deviation
- Standard deviation is never negative
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