You add together all the observations and divide the result by the number of observations.
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The standard deviation.z-score of a value=(that value minus the mean)/(standard deviation)
The standard deviation is a measure of the spread of data about the mean. Although it is essentially a measure of the spread, the fact that it is the spread ABOUT THE MEAN that is being measured means that it does depend on the value of the mean. However, the SD is not affected by a translation of the data. What that means is that if I add any fixed number to each data point, the mean will increase by that number, but the SD will be unchanged.
It is the mode, which is sometimes introduced, along with the mean and median as a measure of "central tendency".
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It is a measure of the spread of the data around its mean value.