Sample Size for a Mean
Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!
Learning zone
Every study design eventually reduces to this line: decide how much error you can live with, decide how confident you want to be, guess the standard deviation, and the sample size falls out. Estimating a mean to within 2 units at 95% confidence when σ ≈ 15 needs n = (1.96 × 15/2)² = 216.09 — always round up, so 217. Rounding down is the classic slip; it leaves you fractionally short of the precision you promised. The σ you plug in is usually borrowed from a pilot study, published literature, or the crude rule that a range spans about four standard deviations.
The square in the formula is the brutal part of research economics. Precision is bought at quadratic cost: tightening E from 2 to 1 in the example above takes the requirement from 217 to 865. Note too that the population size never appears — a well-drawn sample of 1,000 estimates a mean about as well in a city of 100,000 as in a country of 100 million, which is the single most counter-intuitive fact in survey work. Only when the sample is a sizeable fraction of a finite population (over about 5%) does a correction factor start to help you.
- = Required sample size
- = Critical z-value
- = Standard deviation
- = Target margin of error
- Required sample size — Sample Size for a Proportion, Standard Error of the Mean
- Critical z-value — Margin of Error for a Mean, Confidence Interval Lower Limit
- Standard deviation — Z-Score (Standard Score), Variance and Standard Deviation
- Target margin of error — Sample Size for a Proportion, Margin of Error for a Mean