Sample Size Formula n = Z²σ²/E²

Calculate required sample size using n = Z²σ²/E² (continuous outcomes) or n = Z²p(1−p)/E² (proportions), where Z is the critical value, σ is standard deviation, and E is the margin of error. Fundamental research methodology formula.

Data set — comma or newline separated
Statistical Results — n = 8
Count (n)8
Sum (Σx)40
Min2
Max9
Range7
Q14
Q35.5
IQR1.5
Mean (μ)5
Median4.5
Mode4
Pop. Variance (σ²)4
Pop. Std Dev (σ)2
Sample Variance (s²)4.571428571
Sample Std Dev (s)2.138089935
Skewness0.65625
Excess Kurtosis-0.21875
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How It Works

Calculate required sample size using n = Z²σ²/E² (continuous outcomes) or n = Z²p(1−p)/E² (proportions), where Z is the critical value, σ is standard deviation, and E is the margin of error. Fundamental research methodology formula

Each component has a specific meaning:

  • N = Z²σ²/E² or n = Z²p/E² — The n = z²σ²/e² or n = z²p/e² recorded for the scenario being assessed.
  • Where Z is the critical value — The where z is the critical value recorded for the scenario being assessed.
  • Σ is standard deviation — The σ is standard deviation recorded for the scenario being assessed.
  • E is the margin of error — The e is the margin of error recorded for the scenario being assessed.

Note: Interpret the sample size n result against the thresholds and context described above.

How to Use

Enter the n = Z²σ²/E² or n = Z²p/E², where Z is the critical value, σ is standard deviation, E is the margin of error for the scenario you are assessing. Calculate required sample size using n = Z²σ²/E² (continuous outcomes) or n = Z²p(1−p)/E² (proportions), where Z is the critical value, σ is standard deviation, and E is the margin of error. Fundamental research methodology formula. Use the sample size n result to inform your calculation.

Frequently Asked Questions