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Q: What is the relationship between standard deviation and precision?

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is variance the square of the standard deviation

Standard deviation is the square root of the variance.

The standard deviation is the square root of the variance.

There is absolutely no relationship to what you've asked. I'm pretty sure you simply framed the question in the wrong way, but to literally answer your question... none. Zero relationship. There's no such thing. There is however a relationship between standard deviation and a CI, but a CI can in no shape way or form influence a standard deviation.

Standard deviation doesn't have to be between 0 and 1.

Standard deviation is the variance from the mean of the data.

Standard error of the mean (SEM) and standard deviation of the mean is the same thing. However, standard deviation is not the same as the SEM. To obtain SEM from the standard deviation, divide the standard deviation by the square root of the sample size.

The distance between the middle and the inflection point is the standard deviation.

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The mean is the average value and the standard deviation is the variation from the mean value.

It is inversely proportional; a larger standard deviation produces a small kurtosis (smaller peak, more spread out data) and a smaller standard deviation produces a larger kurtosis (larger peak, data more centrally located).

Standard error is the difference between a researcher's actual findings and their expected findings. Standard error measures the accuracy of one's predictions. Standard deviation is the difference between the results of one's experiment as compared with other results within that experiment. Standard deviation is used to measure the consistency of one's experiment.

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