Statistics · Calculator companion · By K Imports
Mean confidence interval, known SD: practical guide
This guide explains how to use the Count.ie mean confidence interval, known sd. Calculate a two-sided normal confidence interval when population SD is known. Follow the inputs, method and worked example below, then compare your own scenario.
Guide written .
Open the Mean confidence interval, known SD calculatorWhat to prepare
- Collect the underlying observations and state how they were sampled.
- Identify the population, sample size and relevant assumptions.
- Check whether observations, probabilities or measurements are independent where the method requires it.
Understand the inputs
- Confidence level
Options: 90%; 95%; 99%.
The calculation method
Mean ± z × known population SD / √n. Use a t method if SD is estimated from the sample.
Worked example
Illustrative inputs and their result.
Example inputs
- Observed sample mean
- 100
- Known population standard deviation
- 15
- Independent sample size
- 100
- Confidence level
- 95%
Calculated example result
- Lower Confidence Bound
- 97.0601
- Upper Confidence Bound
- 102.9399
How to interpret the result
A statistic summarises the supplied data; it does not repair biased sampling or establish causation. Uncertainty depends on the method's assumptions, not just the number of decimal places shown.
Compare equivalent datasets and report the sample size with the result. Where appropriate, test how an outlier or a different uncertainty assumption affects the conclusion.
Common mistakes to avoid
- Do not substitute population and sample definitions without checking the formula.
- Outliers, missing observations and selection bias can change the interpretation.
- A correlation or significance result is not proof of a causal relationship.
Assumptions and sources
Editable inputs are planning assumptions; check the method and result notes for scope.
If your case falls outside this scope, use a more suitable calculator or contact us about an unclear method.