Confidence Interval (Margin of Error)
Calculate the margin of error and confidence interval for a sample mean
Interactive Sandbox
Adjust values in real-time and observe mathematical cause-and-effect
Central Tendency & Dispersion: Measures the central average (mean) and spread of variability (standard deviation).
Variable Mechanics
Roles, constraints & impacts
Sample Mean
Formula Parameter
Standard Deviation (σ)
Formula Parameter
Sample Size
Formula Parameter
Z Value (1.96 for 95%)
Formula Parameter
At a Glance
Gotchas, units & real-world use
Formula Nature & Mechanics
Central Tendency & Dispersion: Measures the central average (mean) and spread of variability (standard deviation).
Common Mistakes & Traps
- Confusing Population Standard Deviation (divide by N) with Sample Standard Deviation (divide by n - 1 for Bessel correction).
- Assuming all distributions are normal (skewed distributions make the median more reliable than mean).
- Outliers disproportionately distort the mean and variance.
Dimensional Analysis & Units
Mean & SD share the same unit as original data; Variance is in [Unit]².
Real-World & Industry Application
Quality control tolerances in manufacturing, stock market volatility metrics, clinical medical trials, and academic grading curves.
Worked Example: Confidence Interval (Margin of Error)
Given:
- mean = 100
- sd = 15
- n = 25
- z = 1.96
- ME = 1.96 × (15 / √25)
- ME = 1.96 × 3
- ME = 5.88
- Interval = 94.12 to 105.88
Answer: 5.88
Frequently Asked Questions
What is the Confidence Interval (Margin of Error) formula?
ME = z × (σ / √n). Calculate the margin of error and confidence interval for a sample mean.
How do I calculate Confidence Interval (Margin of Error)?
Enter Sample Mean (mean), Standard Deviation (σ) (sd), Sample Size (n), Z Value (1.96 for 95%) (z) into the calculator. It applies ME = z × (σ / √n) and shows every step of the working.
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