A Confidence Interval for a Mean Is Not the Spread of All the Measurements

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A report gives an estimated mean with a confidence interval. Those endpoints describe uncertainty in estimating the mean; they are not simply the lowest and highest observations collected.

Find the quantity being estimated

Read the caption and methods for the parameter, interval method and confidence level. NIST’s explanation of confidence limits for a mean distinguishes the estimate from the repeated-sampling interpretation of its interval. A 95% procedure is designed to cover the fixed population mean in 95% of repeated applications under its assumptions.

Ask a separate question about individual values

If you want to know how much the measurements vary, inspect their distribution and appropriate summaries. An interval estimating a mean answers a different question from a prediction interval for a future observation. Neither should be silently relabelled as the observed range.

When noting the result, copy the interval’s full label and its assumptions. Do not treat a narrow interval as proof that sampling was unbiased or measurement was sound. Precision in estimating a quantity cannot repair a poorly chosen question or unrepresentative data.