Variance of Sample Proportion Calculator
The variance of sample proportion is a crucial statistical measure that quantifies the dispersion of a sample proportion around its mean. Understanding and calculating this variance is essential for making informed decisions based on sample data.
- Enter the sample size (n) in the provided field.
- Enter the proportion (p) in the provided field.
- Click the “Calculate” button to compute the variance of sample proportion.
The formula for the variance of sample proportion is:
s² = p(1 - p) / n
Where:
s²is the variance of sample proportion,pis the sample proportion, andnis the sample size.
Real-World Examples
Suppose we have a sample of 100 customers (n = 100) and 40 of them are satisfied with a product (p = 0.4). The variance of sample proportion would be:
s² = 0.4(1 - 0.4) / 100 = 0.0024
Data & Statistics
| Sample Size (n) | Proportion (p) | Variance of Sample Proportion (s²) |
|---|---|---|
| 100 | 0.5 | 0.0025 |
| 500 | 0.3 | 0.0006 |
| 1000 | 0.2 | 0.0002 |
Expert Tips
- Larger sample sizes (n) result in smaller variances, making the sample proportion more precise.
- Proportions closer to 0.5 have smaller variances than proportions closer to 0 or 1.
What is the difference between variance and standard deviation?
The variance is the average of the squared differences from the mean, while the standard deviation is the square root of the variance.