Subjects statistics

Standard Deviation 22E225

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Standard Deviation 22E225


1. The problem asks for the standard deviation, which measures the amount of variation or dispersion in a set of values. 2. The formula for the standard deviation $\sigma$ of a population is: $$\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \mu)^2}$$ where $N$ is the number of data points, $x_i$ are the data points, and $\mu$ is the mean (average) of the data. 3. If you have a sample instead of the whole population, the formula is: $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2}$$ where $n$ is the sample size and $\bar{x}$ is the sample mean. 4. To calculate, first find the mean by adding all data points and dividing by the number of points. 5. Then subtract the mean from each data point and square the result. 6. Sum all squared differences. 7. Divide by $N$ (population) or $n-1$ (sample). 8. Finally, take the square root of that value to get the standard deviation. Since no data was provided, this is the explanation and formula for calculating standard deviation.