Confidence Intervals

What Are Confidence Intervals and How to Calculate Them



Confidence intervals are a powerful tool for making well-informed business decisions. A confidence interval is an interval in which we can be certain of the parameters or values necessary to make accurate and reliable predictions about population parameters. By understanding what a confidence interval is, how it works and its importance to your organization, you'll gain valuable insight into strategic decision-making that can help drive future success.

The Basics of Confidence Intervals:

A Step-by-Step Guide – How to use Confidence Intervals in your Research

In statistics, a confidence interval is a type of estimate used to indicate how reliable an estimate of a population parameter is. This is done by providing a range of possible values likely to contain the population parameter. The confidence level corresponds to the probability that the confidence interval contains the true value of the population parameter.

Confidence intervals are necessary because they help us understand our estimates’ precision. For example, suppose we want to know how much people spend on groceries each week. We could survey a sample of people and calculate the mean (average) amount that they spend. However, we would not expect this value to be exactly equal to the population mean (the average for everyone in the population). This is because our sample may not be representative of the entire population. In other words, some uncertainty is associated with estimating a population parameter from a sample statistic. Confidence intervals provide a way to quantify this uncertainty.

How Confidence Intervals Are Calculated


The first step in calculating a confidence interval is to choose a level of confidence. This corresponds to the probability that the confidence interval will contain the true value of the population parameter. For example, if we wanted to be 95% confident that our interval contained the true population mean, we would say that our confidence level was 95%.

Once you’ve decided on a confidence level, you can use a statistical formula to calculate your confidence interval. The general form for calculating a confidence interval for a population mean is as follows:

Population Mean ± Margin of Error


where Margin of Error = z*σ/√n and z* is the critical value from a standard normal distribution corresponding to your desired confidence level (e.g., z* = 1.96 for 95% confidence). σ is the population standard deviation and n is the sample size.

If you don’t know the population standard deviation, you can use the following formula to calculate it:

σ = √[Σ(X – μ)2/n] where μ is the population mean and X represents each individual value in your sample.



Confidence intervals are an essential statistical tool that allows us to quantify how precise our estimates are. By providing a range of values that are likely to contain the true value of the population parameter, we can get a better understanding of how accurate our estimate really is. While calculating confidence intervals requires more advanced math skills, understanding what they are and how they work can be very helpful in data analysis and interpretation.

Our Newsletter

Reagan Pannell

Reagan Pannell

Reagan Pannell is a highly accomplished professional with 15 years of experience in building lean management programs for corporate companies. With his expertise in strategy execution, he has established himself as a trusted advisor for numerous organisations seeking to improve their operational efficiency.

Jump To Section

Yellow Belt Course

Green Belt Course

LEAN SIX SIGMA Online Courses

A Lean Six Sigma Green Belt Masterclass

only €999

Ready to start your journey into the world of Lean with this free course?


A Lean focused continious improvement certification course

only £119

Propel your career forward, tackle complex problems and drive change

Only £167

The ultimate fast-track for future leadership

only £849

Become an expert in change management and complex problem-solving.

Only £1649

Lean Accelerator Program

discover the power of problem-solving


download the syllabus