Point Estimate Calculator

Best point estimate of a proportion by four methods, or of a mean.

The point estimate of a proportion is p̂ = x ÷ n (the MLE). For 42 successes in 60 trials, p̂ = 0.70. With small samples or extreme proportions, the Wilson estimate (x + z²/2) ÷ (n + z²) is often better. The point estimate of a mean is the sample mean x̄.

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How to use it

  1. Choose proportion or mean.
  2. Enter successes and sample size, or paste the sample values.
  3. Read the point estimates and choose the method that fits your sample.

What you enter

What you get

Formula

MLE = x/n | Wilson = (x + z²/2)/(n + z²) | Laplace = (x + 1)/(n + 2) | Jeffrey = (x + 0.5)/(n + 1)

Worked example

Input: 42 successes, n = 60, 95%

Result: MLE 0.700, Wilson 0.688, Laplace 0.694, Jeffrey 0.697

With p̂ = 0.70 the MLE is the usual choice.

Questions

How do you find a point estimate?

For a proportion, divide successes by trials. For a mean, average the sample values. Each is a single best guess at the population value.

Which point estimate method is best?

Use the MLE when x ÷ n is between 0.5 and 0.9. Use Wilson when it is 0.9 or less in general, Jeffrey for 0.9–0.95, and Laplace above 0.95 (a common rule of thumb).

How do I get a point estimate from a confidence interval?

Take the midpoint: (lower + upper) ÷ 2. The margin of error is (upper − lower) ÷ 2.

Why does the Laplace estimate add 1 and 2?

It adds one success and one failure, which pulls estimates away from 0 and 1 when no failures or no successes were seen.

Limitations

References

Related reading

More Statistics

All free tools · By Dr. Zubair Khalid, DVM, MS, PhD.