Sampling Distribution of the Sample Proportion Calculator

Find the mean and standard error of a sample proportion.

Mean 0.4

Standard error 0.049

Formula: mean = p; SE = √(p(1−p)/n)

Step-by-step with your numbers:

1. Values used:

2. Population proportion = 0.4

3. Sample size = 100

5. Mean = (0.4 / 100) x 100 = 0.004 x 100 = 0.4

6. Standard error = 0.049

Did we solve your problem today?

The distribution of sample proportions is centered on p with a predictable spread.

The math behind it

mean = p, standard error = √(p(1−p)/n). It's approximately normal when np and n(1−p) exceed ~10.

p 0.4, n 100 → mean 0.4, SE ≈ 0.049.

When is it normal?

When both np ≥ 10 and n(1−p) ≥ 10.