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Standard deviation can only be zero if all the data points in your set are equal. If all data points are equal, there is no deviation. For example, if all the participants in a survey coincidentally were all 30 years old, then the value of age would be 30 with no deviation. Thus, there would also be no standard deviation.
A data set of one point (small sample) will always have a standard deviation of zero, because the one value doesn't deviate from itself at all.
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What would it mean if a standard deviation was calculated to equal 0?
A standard deviation of zero means that all the data points are the same value.
Is it true that the standard deviation can equal zero in a data set?
The standard deviation is a measure of how much variation there is in a data set. It can be zero only if all the values are exactly the same - no variation.
Can a standard deviation of a sample be equal to a standard deviation of a population?
Yes
Why use standard deviation and not average deviation?
Because the average deviation will always be zero.
What is the perfect standard normal distribution?
The standard normal distribution is a subset of a normal distribution. It has the properties of mean equal to zero and a standard deviation equal to one. There is only one standard normal distribution and no others so it could be considered the "perfect" one.
What are all the values a standard deviation can take?
The standard deviation must be greater than or equal to zero.
What would it mean if a standard deviation was calculated to equal 0?
A standard deviation of zero means that all the data points are the same value.
Is it true that the standard deviation can equal zero in a data set?
The standard deviation is a measure of how much variation there is in a data set. It can be zero only if all the values are exactly the same - no variation.
What do you do if you are running a comparison to historical data and your background standard deviation is zero?
A standard deviation of 0 implies all of the observations are equal. That is, there is no variation in the data.
Does standard deviation and mean deviation measure dispersion the same?
No. The average of the deviations, or mean deviation, will always be zero. The standard deviation is the average squared deviation which is usually non-zero.
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 a standard deviation of a sample be equal to a standard deviation of a population?
Yes
Why use standard deviation and not average deviation?
Because the average deviation will always be zero.
What is the standard deviation of 3.083065714?
Its zero dummy
Does a zero standard deviation support data?
no
If the standard deviation of 10 scores is 0?
If the standard deviation of 10 scores is zero, then all scores are the same.
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.
