# Standard Deviation Calculator & Concept

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Standard deviation tells you how much a dataset deviates from the mean value.

Paste in as many values as you want!

Standard Deviation (Based on a sample): | - | |

Standard Deviation (Based on a population) | - | |

Variance (Based on a sample) | - | |

Variance (Based on a population) | - | |

Average | - | |

Total Numbers | - |

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.

Single text boxes with number, dollar, or percent validation - Useful to gather income, age, or numbers which require analysis.

Continuous Sum gives deviation for each label - Useful to gather budget data, time allocated to projects, or other numerical allocation questions requiring analysis.