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keisanHigh-precision calculations for everyday life and work

Estimating the true value from the mean and standard deviation

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We estimate the range of the true value using a normal distribution based on the sample mean and standard deviation drawn from the population.
Mean μ
Standard deviation σ
Confidence Level
% 50 < Confidence Level < 100
The true value is ~ and estimate
For a normal distribution, the true value lies within μ±σ with 68.26% confidence, within μ±2σ with 95.45% confidence, and within μ±3σ with 99.73% confidence.

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