Standard Deviation Calculator
Quickly calculate the standard deviation of your dataset and visualize data spread.
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Enter comma-separated numbers to calculate the standard deviation. For example: 2,4,6,8,10
Standard Deviation:
Formula: $$ \sigma = \sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_i - \mu)^2} $$
Data Visualization
Understanding Standard Deviation
Standard Deviation is a measure that shows how much variation or "dispersion" exists from the average (mean, or expected value). A low standard deviation indicates that the data points tend to be very close to the mean, whereas a high standard deviation indicates that the data points are spread out over a wider range of values.
In simpler terms, it's a way to identify how spread out numbers are in a dataset. For instance, if you have test scores, a small standard deviation means most students scored close to the average. A large standard deviation means the scores are more spread out - some very high, some very low.
- Formula: $$ \sigma = \sqrt{\frac{\sum_{i=1}^{N}(x_i - \mu)^2}{N-1}} $$ (for sample standard deviation) where \( \mu \) is the mean, \( x_i \) are the data points, and \( N \) is the number of data points.
- Use Cases: Used in finance, science, and quality control to understand data variability and make informed decisions.
- Learn More: Wikipedia on Standard Deviation