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| − | ====Standard Deviation====
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| − | https://statistics.laerd.com/statistical-guides/measures-of-spread-standard-deviation.php
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| − | The standard deviation is a measure of the spread of scores within a set of data. Usually, we are interested in the standard deviation of a population. However, as we are often presented with data from a sample only, we can estimate the population standard deviation from a sample standard deviation. These two standard deviations - sample and population standard deviations - are calculated differently. In statistics, we are usually presented with having to calculate sample standard deviations, and so this is what this article will focus on, although the formula for a population standard deviation will also be shown.
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| − | <br />
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| − | : '''Population standard deviation''' (<math>\sigma</math>)
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| − | <blockquote>
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| − | <math>\sigma = \sqrt{\frac{\sum_{i=1}^{N}(x_{i} - \mu)^2}{N}}</math>
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| − | <math>\mu: \text{population mean};\ \ \ N: \text{Number of scores in the population}</math>
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| − | </blockquote>
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| − | <br />
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| − | : '''Sample standard deviation formula''' (<math>s</math>)
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| − | <blockquote>
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| − | Sometimes our data is only a sample of the whole population. In this case, we can still estimate the Standard deviation; but when we use a sample as an estimate of the whole population, the Standard deviation formula changes to this:
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| − | <math>s = \sqrt{\frac{\sum_{i=1}^{n}(x_{i} - \bar{x})^2}{n -1}}</math>
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| − | <math>\bar{x}: \text{Sample mean};\ \ \ n: \text{Number of scores in the sample}</math>
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| − | </blockquote>
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| − | <br />
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| − | *The Standard Deviation is the square root of the variance.
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| − | *This measure is the most widely used to express deviation from the mean in a variable.
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| − | *The higher the value the more widely distributed are the variable data values around the mean.
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| − | *Assuming the frequency distributions approximately normal, about 68% of all observations are within +/- 1 standard deviation.
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| − | *Approximately 95% of all observations fall within two standard deviations of the mean (if data is normally distributed).
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