---
url: "https://questionstar.com/principles-of-survey-research/chapter-4/slide-145.html"
title: "How Large Must the Sample Be?"
type: "lehrbuch-slide"
chapter: 4
chapterTitle: "Sampling"
slide: 145
---

# How Large Must the Sample Be?

*The higher the desired accuracy, the larger the sample must be.*

![E ≈ 1/√n ⇒ n ≈ (1/E)²](/principles-of-survey-research/media/formel_n_aus_e.png)

The higher the desired accuracy, the larger the sample must be.

± 1 %

n = (1 / 0.01)² = 100²

10.000

± 2 %

n = (1 / 0.02)² = 50²

2.500

± 5 %

n = (1 / 0.05)² = 20²

± 10 %

n = (1 / 0.1)² = 10²

Doubling the accuracy costs four times the sample. The size does not depend on the size of the population.

Calculations show approximate values for a 95% confidence level

---

*Slide 145 of 274 · Chapter 4: Sampling · Principles of Survey Research · Dr. Paul Marx*