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Can standard deviation be a negative?

Updated: 4/28/2022
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No. Standard deviation is the square root of a non-negative number (the variance) and as such has to be at least zero. Please see the related links for a definition of standard deviation and some examples.

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Q: Can standard deviation be a negative?
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Is it possible for a standard deviation to be negative?

no it is not possible because you have to take the square of error that is (x-X)2. the square of any number is always positive----------Improved answer:It is not possible to have a negative standard deviation because:SD (standard deviation) is equal to the square of V (variance).


What are the assumptions of standard deviation?

The standard deviation is the standard deviation! Its calculation requires no assumption.


How does one interpret a standard deviation which is more than the mean?

Standard deviation is a measure of the dispersion of the data. When the standard deviation is greater than the mean, a coefficient of variation is greater than one. See: http://en.wikipedia.org/wiki/Coefficient_of_variation If you assume the data is normally distributed, then the lower limit of the interval of the mean +/- one standard deviation (68% confidence interval) will be a negative value. If it is not realistic to have negative values, then the assumption of a normal distribution may be in error and you should consider other distributions. Common distributions with no negative values are gamma, log normal and exponential.


What is the difference between standard error of mean and standard deviation of means?

Standard error of the mean (SEM) and standard deviation of the mean is the same thing. However, standard deviation is not the same as the SEM. To obtain SEM from the standard deviation, divide the standard deviation by the square root of the sample size.


What does a negative deviation mean?

A negative deviation means that the observation is smaller than whatever it is that the deviation is being measured from.

Related questions

What can cause standard deviation to be negative?

Standard deviation can never be negative.


Can standard deviation and variance be negative?

No. Neither the standard deviation nor the variance can ever be negative.


Would the mean and standard deviation be negative if the set has only negative values?

The mean would be negative, but standard deviation is always positive.


How do you know if a z score is positive or negative?

A negative Z-Score corresponds to a negative standard deviation, i.e. an observation that is less than the mean, when the standard deviation is normalized so that the standard deviation is zero when the mean is zero.


What if the standard deviation is negative?

There is a calculation error.


Can The standard deviation of a distribution be a negative value?

No. The standard deviation is not exactly a value but rather how far a score deviates from the mean.


Is it possible for a standard deviation to be negative?

no it is not possible because you have to take the square of error that is (x-X)2. the square of any number is always positive----------Improved answer:It is not possible to have a negative standard deviation because:SD (standard deviation) is equal to the square of V (variance).


Can the standard deviation or variance be negative?

No, a standard deviation or variance does not have a negative sign. The reason for this is that the deviations from the mean are squared in the formula. Deviations are squared to get rid of signs. In Absolute mean deviation, sum of the deviations is taken ignoring the signs, but there is no justification for doing so. (deviations are not squared here)


What are the assumptions of standard deviation?

The standard deviation is the standard deviation! Its calculation requires no assumption.


Can Standard Deviation be greater than 100?

Yes. It can have any non-negative value.


What does the sample standard deviation best estimate?

The standard deviation of the population. the standard deviation of the population.


Can standard deviation assume a negative value?

No. It is defined to be the positive square root of ((the sum squared deviation divided by (the number of observations less one))