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Is it true that the standard deviation is equal to the square root of the variance?
Wiki User
∙ 12y ago
Yes. Please see the related link, below.
Wiki User
∙ 12y ago
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The square of the standard deviation is equal to?
The variance
Can standard deviation equals to variance?
The variance is the square of the standard deviation.This question is equivalent tocan s = s^2The answer is yes, but only in two cases.If the standard deviation is 1 exactly, then so is the variance.If the standard deviation is 0 exactly, then so is the variance.If the standard deviation is anything else, then it is not equal to the variance.You are not likely to find these special cases in practical problems, so from a practical sense, you should think that they are generally not equal.
Can the variance be zero?
Variance is standard deviation squared. If standard deviation can be zero then the variance can obviously be zero because zero squared is still zero. The standard deviation is equal to the sum of the squares of each data point in your data set minus the mean, all that over n. The idea is that if all of your data points are the same then the mean will be the same as every data point. If the mean is the equal to every data point then the square of each point minus the mean would be zero. All of the squared values added up would still be zero. And zero divided by n is still zero. In this case the standard deviation would be zero. Short story short: if all of the points in a data set are equal than the variance will be zero. Yes the variance can be zero.
Can standard deviation equal standard error?
If n = 1.
If the standard error of a sample of 48 is equal to 14.25 the standard deviation is equal to?
98.73
The square of the standard deviation is equal to?
The variance
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 value of the variance ever equal the value of the standard deviation?
Yes; when the variance is one.
What is the equation for standard deviation?
Standard deviation is equal to the square root of the variance. To arrive at this work out the mean, then subtract the mean and square the result of each number. Then work out the mean of those squared differences and take the square root of that.
Why the standard deviation of a set of data will always be greater than or equal to 0?
Because it is defined as the principal square root of the variance.
Can standard deviation equals to variance?
The variance is the square of the standard deviation.This question is equivalent tocan s = s^2The answer is yes, but only in two cases.If the standard deviation is 1 exactly, then so is the variance.If the standard deviation is 0 exactly, then so is the variance.If the standard deviation is anything else, then it is not equal to the variance.You are not likely to find these special cases in practical problems, so from a practical sense, you should think that they are generally not equal.
What is the relationship between the mean and standard deviation in statistics?
The 'standard deviation' in statistics or probability is a measure of how spread out the numbers are. It mathematical terms, it is the square root of the mean of the squared deviations of all the numbers in the data set from the mean of that set. It is approximately equal to the average deviation from the mean. If you have a set of values with low standard deviation, it means that in general, most of the values are close to the mean. A high standard deviation means that the values in general, differ a lot from the mean. The variance is the standard deviation squared. That is to say, the standard deviation is the square root of the variance. To calculate the variance, we simply take each number in the set and subtract it from the mean. Next square that value and do the same for each number in the set. Lastly, take the mean of all the squares. The mean of the squared deviation from the mean is the variance. The square root of the variance is the standard deviation. If you take the following data series for example, the mean for all of them is '3'. 3, 3, 3, 3, 3, 3 all the values are 3, they're the same as the mean. The standard deviation is zero. This is because the difference from the mean is zero in each case, and after squaring and then taking the mean, the variance is zero. Last, the square root of zero is zero so the standard deviation is zero. Of note is that since you are squaring the deviations from the mean, the variance and hence the standard deviation can never be negative. 1, 3, 3, 3, 3, 5 - most of the values are the same as the mean. This has a low standard deviation. In this case, the standard deviation is very small since most of the difference from the mean are small. 1, 1, 1, 5, 5, 5 - all the values are two higher or two lower than the mean. This series has the highest standard deviation.
Can the variance be zero?
Variance is standard deviation squared. If standard deviation can be zero then the variance can obviously be zero because zero squared is still zero. The standard deviation is equal to the sum of the squares of each data point in your data set minus the mean, all that over n. The idea is that if all of your data points are the same then the mean will be the same as every data point. If the mean is the equal to every data point then the square of each point minus the mean would be zero. All of the squared values added up would still be zero. And zero divided by n is still zero. In this case the standard deviation would be zero. Short story short: if all of the points in a data set are equal than the variance will be zero. Yes the variance can be zero.
Are the mean and standard deviation equal in a poisson distribution?
The mean and variance are equal in the Poisson distribution. The mean and std deviation would be equal only for the case of mean = 1. See related link.
Can a standard deviation of a sample be equal to a standard deviation of a population?
Yes
What are all the values a standard deviation can take?
The standard deviation must be greater than or equal to zero.
Can standard deviation equal standard error?
If n = 1.
