Standard Deviation Calculator & Concept
The above example can be condensed to the following formulas:
Population Standard Deviation
Sample Standard Deviation
Standard deviation is a measure that is used to quantify the amount of variation or dispersion of a set of data values. The standard deviation is a description of the data's spread, how widely it is distributed about the mean. A smaller standard deviation indicates that more of the data is clustered about the mean. A larger one indicates the data are more spread out.
Generally speaking data is normally distributed. This is important as it can be inferred that normally distributed data follows a bell shaped curve. That bell happened curve can tell us more about our data.
The above graph shows the rules for normally distributed data. 68% of responses are within 1 deviation of the mean, 95% of responses are within 2 deviations of the mean, while 99.7% of the data is within 3 deviations of the mean.
Example: If a question asks for monthly income the mean could be $35,000 with a standard deviation of $5,000. We could assume that 68% of total responses fall somewhere between $30,000 and $40,000. We could also assume 95% of the data falls between $25,000 and $45,000. From this you can infer what people to target if your survey was looking what customers to sell to.