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Q: Is sigma the same thing as standard deviation?

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No.

Standard error of the mean (SEM) and standard deviation of the mean is the same thing. However, standard deviation is not the same as the SEM. To obtain SEM from the standard deviation, divide the standard deviation by the square root of the sample size.

yes, h=1/sigma(standard deviation)

No. But they are related. If a sample of size n is taken, a standard deviation can be calculated. This is usually denoted as "s" however some textbooks will use the symbol, sigma. The standard deviation of a sample is usually used to estimate the standard deviation of the population. In this case, we use n-1 in the denomimator of the equation. The variance of the sample is the square of the sample's standard deviation. In many textbooks it is denoted as s2. In denoting the standard deviation and variance of populations, the symbols sigma and sigma2 should be used. One last note. We use standard deviations in describing uncertainty as it's easier to understand. If our measurements are in days, then the standard deviation will also be in days. The variance will be in units of days2.

The standard deviation is defined as the square root of the variance, so the variance is the same as the squared standard deviation.

Standard deviation has the same unit as the data set unit.

The smaller the standard deviation, the closer together the data is. A standard deviation of 0 tells you that every number is 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.

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

The standard deviation is the square root of the variance.

If repeated samples are taken from a population, then they will not have the same mean each time. The mean itself will have some distribution. This will have the same mean as the population mean and the standard deviation of this statistic is the standard deviation of the mean.

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