How to Calculate 95% Confidence Limits


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 - 1.96SE and M + 1.96SE for the left- and right-hand side confidence limits.


  • Photo Credit Jupiterimages/Goodshoot/Getty Images
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