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FutureStarrA S to D Calculator
S to D Calculator is here to help you master everyday tasks. Drag the slider to convert measurements from inches to centimeters or from kilometers to miles per hour.
Standard deviation in statistics, typically denoted by σ, is a measure of variation or dispersion (refers to a distribution's extent of stretching or squeezing) between values in a set of data. The lower the standard deviation, the closer the data points tend to be to the mean (or expected value), μ. Conversely, a higher standard deviation indicates a wider range of values. Similar to other mathematical and statistical concepts, there are many different situations in which standard deviation can be used, and thus many different equations. In addition to expressing population variability, the standard deviation is also often used to measure statistical results such as the margin of error. When used in this manner, standard deviation is often called the standard error of the mean, or standard error of the estimate with regard to a mean. The calculator above computes population standard deviation and sample standard deviation, as well as confidence interval approximations.
The next example is one third. If you use SD to switch to a decimal, you get a recurring decimal in the first instance. This is 0.3 with a dot above the recurring part, in this case the 3. On some models, particularly the US model of this calculator, the 300ES Plus, have a line above the recurrence instead of a dot. Press SD again and you get a full calculator display decimal approximation. (Source: thecalculatorguide.com)
In many cases, it is not possible to sample every member within a population, requiring that the above equation be modified so that the standard deviation can be measured through a random sample of the population being studied. A common estimator for σ is the sample standard deviation, typically denoted by s. It is worth noting that there exist many different equations for calculating sample standard deviation since, unlike sample mean, sample standard deviation does not have any single estimator that is unbiased, efficient, and has a maximum likelihood. The equation provided below is the "corrected sample standard deviation." It is a corrected version of the equation obtained from modifying the population standard deviation equation by using the sample size as the size of the population, which removes some of the bias in the equation. Unbiased estimation of standard deviation, however, is highly involved and varies depending on the distribution. As such, the "corrected sample standard deviation" is the most commonly used estimator for population standard deviation, and is generally referred to as simply the "sample standard deviation." It is a much better estimate than its uncorrected version, but still has a significant bias for small sample sizes (N<10).
Standard deviation is widely used in experimental and industrial settings to test models against real-world data. An example of this in industrial applications is quality control for some products. Standard deviation can be used to calculate a minimum and maximum value within which some aspect of the product should fall some high percentage of the time. In cases where values fall outside the calculated range, it may be necessary to make changes to the production process to ensure quality control. (Source: www.calculator.net)