A confidence interval is related to distribution. A confidence interval is established so that we can determine the confidence with which it can be said that a data point lies within a specified interval around the mean.

Confidence interval is usual given by the formula: estimate +/- margin of error.

Closely related to confidence intervals is the concept of standard deviation. Simply put, standard deviation is the square root of the variance (the link below includes the lengthy square root formula).

One standard deviation corresponds to a 68% confidence interval.

A sample problem is as follows: If 1,000 people went shopping, and 64% claim to have spent more than $25, the 99% percent confidence interval could be determined by using (.64) for xi and (.36) for (1-xi), and n=1,000: sqrt((.64)(.36)/1,000)~.015.

Now, 99% of the population should be within 2.576 standard deviations of the mean, thus, .64 +/- (.015)(2.576)= .64 +/- .03846 is the interval. This means that it is 99% certain that .64 +/- .03846 spent more than $25.

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**Further Reading**