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Can The standard deviation of a distribution be a negative value?
Wiki User
∙ 14y ago
No. The standard deviation is not exactly a value but rather how far a score deviates from the mean.
Wiki User
∙ 14y ago
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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.
Is standard deviation an absolute value?
No. Standard deviation is not an absolute value. The standard deviation is often written as a single positive value (magnitude), but it is really a binomial, and it equals both the positive and negative of the given magnitude. For example, if you are told that for a population the SD is 5.0, it really means +5.0 and -5.0 from the population mean. It defines a region within the distribution, starting at the lower magnitude (-5.0) increasing to zero (the mean), and another region starting at zero (the mean) and increasing up to the upper magnitude (+5.0). Both regions together define the (continuous) region of standard deviation 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.
What is the z value for a normal distribution?
If a random variable X has a Normal distribution with mean m and standard deviation s, then z = (X - m)/s has a Standard Normal distribution. That is, Z has a Normal distribution with mean 0 and standard deviation 1. Probabilities for a general Normal distribution are extremely difficult to obtain but values for the Standard Normal have been calculated numerically and are widely tabulated. The z-transformation is, therefore, used to evaluate probabilities for Normally distributed random variables.
Why is it a useful value to report standard deviation?
The standard deviation of a distribution is the average spread from the mean (average). If I told you I had a distribution of data with average 10000 and standard deviation 10, you'd know that most of the data is close to the middle. If I told you I had a distrubtion of data with average 10000 and standard deviation 3000, you'd know that the data in this distribution is much more spread out. dhaussling@gmail.com
Can standard deviation value be less than 01?
Yes, it can have any non-negative value.
What are importance of mean and standard deviation in the use of normal distribution?
For data sets having a normal distribution, the following properties depend on the mean and the standard deviation. This is known as the Empirical rule. About 68% of all values fall within 1 standard deviation of the mean About 95% of all values fall within 2 standard deviation of the mean About 99.7% of all values fall within 3 standard deviation of the mean. So given any value and given the mean and standard deviation, one can say right away where that value is compared to 60, 95 and 99 percent of the other values. The mean of the any distribution is a measure of centrality, but in case of the normal distribution, it is equal to the mode and median of the distribtion. The standard deviation is a measure of data dispersion or variability. In the case of the normal distribution, the mean and the standard deviation are the two parameters of the distribution, therefore they completely define the distribution. See: http://en.wikipedia.org/wiki/Normal_distribution
What do standard deviation error bars indicate when they go past your minimum value?
If the minimum value is the minimum observed value then it indicates that the distribution goes below the minimum observed value.If the minimum value is the minimum defined for the distribution then it indicates thatthe data do not come from the proposed distribution,estimates for the mean or standard deviation are incorrect, oryou have got a sample which is atypical.
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.
In a standard normal distribution what is the value of the mean and standard deviation?
idk about normal distribution but for Mean "M" = (overall sum of "x") / "n" frequency distribution: 'M' = Overall sum of (' x ' * ' f ') / overall sum of ( ' f ' ) M = Mean x = Mid Point f = frequiency n = number of variables ALL FOR STANDARD DEVIATION * * * * * A general Normal distribution is usually described in terms of its parameters, and given as N(mu, sigma2) where mu is the mean and sigma is the standard deviation. The STANDARD Normal distribution is the N(0, 1) distribution, that is, it has mean = 0 and variance (or standard deviation) = 1.
What are all the values that a standard deviation s can possibly take?
Any non-negative value.
What is the z score of 1.0?
It is the value that is one standard deviation greater than the mean of a Normal (Gaussian) distribution.
Is standard deviation an absolute value?
No. Standard deviation is not an absolute value. The standard deviation is often written as a single positive value (magnitude), but it is really a binomial, and it equals both the positive and negative of the given magnitude. For example, if you are told that for a population the SD is 5.0, it really means +5.0 and -5.0 from the population mean. It defines a region within the distribution, starting at the lower magnitude (-5.0) increasing to zero (the mean), and another region starting at zero (the mean) and increasing up to the upper magnitude (+5.0). Both regions together define the (continuous) region of standard deviation from the mean 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.
Can the variance of a normally distributed random variable be negative?
No. The variance of any distribution is the sum of the squares of the deviation from the mean. Since the square of the deviation is essentially the square of the absolute value of the deviation, that means the variance is always positive, be the distribution normal, poisson, or other.
