How to Calculate 95% Confidence Limits

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Variation in the distribution of a statistical variable is called the measure of dispersion. The standard deviation of a distribution that consists of an aggregation of averages is called the standard error. A normal distribution contains at least 100 samples. 95 percent confidence limits define the 95 percent confidence interval boundaries. For a normal distribution, the mean of the distribution is between these confidence interval boundaries 95 percent of the time.

Calculate "M," or the mean of the normal distribution, by adding all the data values and dividing them by the total number of data points.

Calculate "SE," or the standard deviation of the normal distribution, by subtracting the average from each data value, squaring the result and taking the average of all the results.

Calculate the 95 percent confidence limits with the formulas M - 1.96_SE and M + 1.96_SE for the left- and right-hand side confidence limits.

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