Statistics

Point Estimate Calculator

Estimate a population proportion using several methods.

Calculated Output

MLE estimate 0.4

Laplace estimate 0.402

Wilson estimate 0.4037

Formula: MLE = x/n; Laplace = (x+1)/(n+2); Wilson midpoint

Step-by-Step Breakdown

1. Values used:

2. Successes = 40

3. Trials = 100

5. MLE estimate = Successes / Trials = 40 / 100 = 0.4

6. Laplace estimate = 0.402

7. Wilson estimate = 0.4037

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The math behind it

The MLE is x/n. Laplace and Wilson estimates shrink extreme proportions toward 0.5 for stability.

40 of 100 gives MLE 0.40, Wilson about 0.404.

Why use Wilson?

It behaves better than the simple proportion for small samples or extreme values.