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Q: Does a zero standard deviation support data?

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No. Variance and standard deviation are dependent on, but calculated irrespective of the data. You do, of course, have to have some variation, otherwise, the variance and standard deviation will be zero.

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.

A standard deviation of 0 implies all of the observations are equal. That is, there is no variation in the data.

A standard deviation of zero means that all the data points are the same value.

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.

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.!

Either when there is a single data item, or when all data items have exactly the same value.

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.

Because the average deviation will always be zero.

The standard deviation must be greater than or equal to zero.

Yes. Standard deviation depends entirely upon the distribution; it is a measure of how spread out it is (ie how far from the mean "on average" the data is): the larger it is the more spread out it is, the smaller the less spread out. If every data point was the mean, the standard deviation would be zero!

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.

Its zero dummy

If the standard deviation of 10 scores is zero, then all scores are the same.

Yes, but only if every element in the data set is exactly the same. Therefore, very unlikely.

This means that the set of data is clustered really close to the mean/average. Your data set likely has a small range (highest value - lowest value). In other words, if the average is 6.3, and the standard deviation is 0.7, this means that each individual piece of data, on average, is different from the mean by 0.7. Each piece of data deviates from the mean by an average (standard) of 0.7; hence standard deviation! By definition, 66% of all data is 1 standard deviation from the mean, so 66% of the data in this example would be between the values of 5.6 and 7.0.

The standard deviation is always be equal or higher than zero. If my set of data is limited to whole numbers, all of which are equal, the standard deviation is 0. In all other situations, we first calculate the difference of each number from the average and then calculate the square of the difference. While the difference can be a negative, the square of the difference can not be. The square of the standard deviation has to be positive, since it is the sum of all positive numbers. If we calculate s2 = 4, then s can be -2 or +2. By convention, we take the positive root.

ZeroDetails:The "Standard Deviation" for ungrouped data can be calculated in the following steps:all the deviations (differences) from the arithmetic mean of the set of numbers are squared;the arithmetic mean of these squares is then calculated;the square root of the mean is the standard deviationAccordingly,The arithmetic mean of set of data of equal values is the value.All the deviations will be zero and their squares will be zerosThe mean of squares is zeroThe square root of zero is zero which equals the standard deion

[10, 10, 10, 10, 10, 10, 10] has a mean of 10 and a standard deviation of zero.

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.

Yes. It all the observed values are exactly the same then the SD will be 0.

It is always zero.

It is zero.

Simple! The average deviation for any data set is zero - by definition.

There is 1) standard deviation, 2) mean deviation and 3) mean absolute deviation. The standard deviation is calculated most of the time. If our objective is to estimate the variance of the overall population from a representative random sample, then it has been shown theoretically that the standard deviation is the best estimate (most efficient). The mean deviation is calculated by first calculating the mean of the data and then calculating the deviation (value - mean) for each value. If we then sum these deviations, we calculate the mean deviation which will always be zero. So this statistic has little value. The individual deviations may however be of interest. See related link. To obtain the means absolute deviation (MAD), we sum the absolute value of the individual deviations. We will obtain a value that is similar to the standard deviation, a measure of dispersal of the data values. The MAD may be transformed to a standard deviation, if the distribution is known. The MAD has been shown to be less efficient in estimating the standard deviation, but a more robust estimator (not as influenced by erroneous data) as the standard deviation. See related link. Most of the time we use the standard deviation to provide the best estimate of the variance of the population.