Confidence Interval

Learn about confidence interval, the central limit theorem, and their relationships with standard deviation.

Understanding the concept

Confidence interval is a critical concept in inferential statistics. It estimates the range of plausible values for a population parameter based on a data sample. Confidence intervals provide a way to quantify the uncertainty associated with point estimates. We use standard deviation to define confidence intervals.

Suppose we gather the math test scores of high school students in a country, and we wish to determine the 95% confidence interval of the population mean. We collect a random sample of 200 high school students from across the country and use their scores in the calculation.

The calculation result means that we can be 95% confident that the average score on the math exam for all high school students in the country falls between the lower and upper range of the confidence interval.

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Normally distributed data
Normally distributed data

This method allows us to make inferences about the average math score of all high school students in the country by looking at a small sample which relieves us from spending a vast amount of time and resources.

To calculate the confidence interval of the data, we use the following formula. The formula uses the mean and standard deviations of the data.

In the confidence interval formula:

  • xˉ\bar{x} ...