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No. It is defined to be the positive square root of ((the sum squared deviation divided by (the number of observations less one))
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What is the difference between standard deviation and mean?
The mean is the average value and the standard deviation is the variation from the mean value.
Sample standard deviation?
Standard deviation in statistics refers to how much deviation there is from the average or mean value. Sample deviation refers to the data that was collected from a smaller pool than the population.
How standard deviation and Mean deviation differ from each other?
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.
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.
What happens to the standard score as the standard deviation increases?
The absolute value of the standard score becomes smaller.
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.
Can standard deviation value be less than 01?
Yes, it can have any non-negative value.
Can Standard Deviation be greater than 100?
Yes. It can have any non-negative value.
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 are all the values that a standard deviation s can possibly take?
Any non-negative value.
What does a negative z-score mean?
z-score of a value=(that value minus the mean)/(standard deviation). So if a value has a negative z-score, then it is below the mean.
What is the difference between standard deviation and mean?
The mean is the average value and the standard deviation is the variation from the mean value.
Can standard deviation value be bigger than maximum and minimum value?
No standard deviation can not be bigger than maximum and minimum values.
Is variance square of standard deviation?
Yes, the variance of a data set is the square of the standard deviation (sigma) of the set. This means that the variance is always a positive number, even though the data might have a negative sigma value.
Sample standard deviation?
Standard deviation in statistics refers to how much deviation there is from the average or mean value. Sample deviation refers to the data that was collected from a smaller pool than the population.
Can average deviation be negative?
No, average deviation cannot be negative. Deviation is a representation of differences between numbers. A difference is always an absolute value, so the number cannot be negative (even though subtracting the deviation from an average may result in a a negative result).
Is the expected value the same as the standard deviation?
No. The expected value is the mean!
