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Matematik

Sample Size Calculator

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Nedir Sample Size Calculator?

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Sample size is the number of observations needed to estimate a population parameter within a specified margin of error at a given confidence level. Larger samples give more precise estimates, but the relationship is not linear — quadrupling the sample only halves the margin of error.

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Nasıl Sample Size Calculator

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  1. 1Determine your confidence level (usually 95%) and margin of error (usually ±5%)
  2. 2Estimate the proportion p (use 50% if unknown — gives the most conservative/largest sample)
  3. 3Formula: n = z²×p×(1−p) / e²
  4. 4For finite populations, apply correction: n_adjusted = n / (1 + (n−1)/N)

Çözümlü Örnekler

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Örnek 1
Verilen:95% CI, ±5% margin, unknown proportion
Sonuç:n = 385

The standard "385 rule" for large populations

Örnek 2
Verilen:99% CI, ±3% margin
Sonuç:n = 1,844

Higher confidence and precision requires much larger sample

Sample Size Quick Reference (95% CI)

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Margin of Errorp=50% (worst case)p=30%p=10%
±1%9,6048,0683,457
±2%2,4012,017864
±3%1,068897384
±5%385323138
±10%978135
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Uzman İpucu

Always recruit slightly more than your target sample size to account for non-response and dropout. A 20% buffer is common in research.

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Biliyor muydunuz?

National polls of 1,000–1,500 people can represent a country of 300 million with only ±3% margin of error. The key is random selection — a biased sample of 1 million is worse than a random sample of 1,000.

Mathematically verified
Reviewed October 2026
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