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I am not entirely sure I understand correctly what you mean by "essence". However, the idea of finding the standard deviation is to determine, as a general tendency, whether most data points are close to the average, or whether there is a large spread in the data. The standard deviation means, more or less, "How far is the typical data point from the average?"

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Q: What is the essence of finding the standard deviation of your data?

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Standard deviation is a measure of the spread of data.

The standard deviation is a measure of the spread of data.

No, if the standard deviation is small the data is less dispersed.

Standard deviation is a measure of variation from the mean of a data set. 1 standard deviation from the mean (which is usually + and - from mean) contains 68% of the data.

Standard deviation is the variance from the mean of the data.

No. Variance and standard deviation are dependent on, but calculated irrespective of the data. You do, of course, have to have some variation, otherwise, the variance and standard deviation will be zero.

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.

A large standard deviation means that the data were spread out. It is relative whether or not you consider a standard deviation to be "large" or not, but a larger standard deviation always means that the data is more spread out than a smaller one. For example, if the mean was 60, and the standard deviation was 1, then this is a small standard deviation. The data is not spread out and a score of 74 or 43 would be highly unlikely, almost impossible. However, if the mean was 60 and the standard deviation was 20, then this would be a large standard deviation. The data is spread out more and a score of 74 or 43 wouldn't be odd or unusual at all.

no

Standard Deviation tells you how spread out the set of scores are with respects to the mean. It measures the variability of the data. A small standard deviation implies that the data is close to the mean/average (+ or - a small range); the larger the standard deviation the more dispersed the data is from the mean.

The standard deviation of a set of data is a measure of the spread of the observations. It is the square root of the mean squared deviations from the mean of the data.

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