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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

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Q: Why is it a useful value to report standard deviation?

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The mean is the average value and the standard deviation is the variation from the mean value.

No. The standard deviation is not exactly a value but rather how far a score deviates from the mean.

No standard deviation can not be bigger than maximum and minimum values.

No. The expected value is the mean!

Standard Deviation = (principal value of) the square root of Variance. So SD = 10.

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.

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

The standard deviation.z-score of a value=(that value minus the mean)/(standard deviation)

The absolute value of the standard score becomes smaller.

Yes; when the variance is one.

Yes is possible for 4.34 to be a standard deviation for a set of numbers. The set of numbers will determine what it is, but that is a perfectly valid value.

The larger the value of the standard deviation, the more the data values are scattered and the less accurate any results are likely to be.

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