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What else can I help you with?
Can the standard deviation or variance be negative?
No, a standard deviation or variance does not have a negative sign. The reason for this is that the deviations from the mean are squared in the formula. Deviations are squared to get rid of signs. In Absolute mean deviation, sum of the deviations is taken ignoring the signs, but there is no justification for doing so. (deviations are not squared here)
What does it mean normal distribution?
The Normal distribution is a probability distribution of the exponential family. It is a symmetric distribution which is defined by just two parameters: its mean and variance (or standard deviation. It is one of the most commonly occurring distributions for continuous variables. Also, under suitable conditions, other distributions can be approximated by the Normal. Unfortunately, these approximations are often used even if the required conditions are not met!
What is the square root of the average of the squared deviations from the mean?
It is the standard deviation.
What percent of data falls between 1 Standard deviation below and 2 stand deviations above the mean?
The answer will depend on what the distribution is. Non-statisticians often assum that the variable that they are interested in follows the Standard Normal distribution. This assumption must be justified. If that is the case then the answer is 81.9%
Is standard deviation the arithmetic mean of the squared deviations from the means?
No. Standard deviation is the square root of the mean of the squared deviations from the mean. Also, if the mean of the data is determined by the same process as the deviation from the mean, then you loose one degree of freedom, and the divisor in the calculation should be N-1, instead of just N.
What is the difference between t-distribution and standard normal distribution?
the t distributions take into account the variability of the sample standard deviations. I think that it is now common to use the t distribution when the population standard deviation is unknown, regardless of the sample size.
How do you find highest standard deviation in given number?
Standard deviations are measures of data distributions. Therefore, a single number cannot have meaningful standard deviation.
How do you derive the mean deviation about the mean of the pareto type 1 distributions?
Easy. The mean deviation about the mean, for any distribution, MUST be 0.
Do some normal probability distributions have different means and different standard deviations?
Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.
Why standard deviation is best measure of dispersion?
standard deviation is best measure of dispersion because all the data distributions are nearer to the normal distribution.
Why normality is required for standard deviation application?
Because the z-score table, which is heavily related to standard deviation, is only applicable to normal distributions.
Can the standard deviation or variance be negative?
No, a standard deviation or variance does not have a negative sign. The reason for this is that the deviations from the mean are squared in the formula. Deviations are squared to get rid of signs. In Absolute mean deviation, sum of the deviations is taken ignoring the signs, but there is no justification for doing so. (deviations are not squared here)
Difference between standard deviation and mean devition?
The mean deviation (also called the mean absolute deviation) is the mean of the absolute deviations of a set of data about the data's mean. The standard deviation sigma of a probability distribution is defined as the square root of the variance sigma^2,
What does standard deviation help you find?
Standard deviation helps you identify the relative level of variation from the mean or equation approximating the relationship in the data set. In a normal distribution 1 standard deviation left or right of the mean = 68.2% of the data 2 standard deviations left or right of the mean = 95.4% of the data 3 standard deviations left or right of the mean = 99.6% of the data
What happens in a normal distribution when the means are equal but the standard deviation changes?
The two distributions are symmetrical about the same point (the mean). The distribution where the sd is larger will be more flattened - with a lower peak and more spread out.
The mean plus or minus the standard deviation for a normal distribution provides a probability range of what percent?
in a normal distribution, the mean plus or minus one standard deviation covers 68.2% of the data. If you use two standard deviations, then you will cover approx. 95.5%, and three will earn you 99.7% coverage
Why use the squarred version of the sum of deviations from the mean?
You cannot use deviations from the mean because (by definition) their sum is zero. Absolute deviations are one way of getting around that problem and they are used. Their main drawback is that they treat deviations linearly. That is to say, one large deviation is only twice as important as two deviations that are half as big. That model may be appropriate in some cases. But in many cases, big deviations are much more serious than that a squared (not squarred) version is more appropriate. Conveniently the squared version is also a feature of many parametric statistical distributions and so the distribution of the "sum of squares" is well studied and understood.
