± 误差范围计算器（调查抽样）Margin of Error Calculator (Surveys)
输入样本量、置信水平和样本比例，计算调查结果的误差范围 ± z·√(p(1 − p)/n)，可填总体规模做有限总体校正，并给出置信区间。Calculate a survey's margin of error, ± z·√(p(1 − p)/n), from the sample size, confidence level and sample proportion, with an optional finite-population correction and the confidence interval.
使用说明与常见问题How-to & FAQ
「误差范围计算器（调查抽样）」是什么？What is the Margin of Error Calculator (Surveys) tool?
输入样本量、置信水平和样本比例，计算调查结果的误差范围 ± z·√(p(1 − p)/n)，可填总体规模做有限总体校正，并给出置信区间。Calculate a survey's margin of error, ± z·√(p(1 − p)/n), from the sample size, confidence level and sample proportion, with an optional finite-population correction and the confidence interval.
如何使用「误差范围计算器（调查抽样）」？How do I use the Margin of Error Calculator (Surveys) tool?
在「误差范围计算器（调查抽样）」中，填写「样本量 n」、「置信水平」、「样本比例 %（不知道时用 50）」、「总体规模（可选）」等参数，结果会随输入实时计算并显示在下方。In the Margin of Error Calculator (Surveys): Fill in "Sample size n", "Confidence level", "Sample proportion % (use 50 if unknown)", "Population size (optional)"; results are recalculated instantly as you type.
误差范围怎么算？How is the margin of error calculated?
E = z × √(p(1 − p) ÷ n)，95% 置信水平 z = 1.96。总体不大时乘以有限总体校正 √((N − n) ÷ (N − 1))。E = z × √(p(1 − p) ÷ n), with z = 1.96 at 95% confidence. For a small population it is multiplied by the finite-population correction √((N − n) ÷ (N − 1)).
为什么默认 50%？Why 50% by default?
p = 50% 时 p(1 − p) 最大，误差范围最保守。调查报告里的「误差 ±3%」通常就是按 50% 算的。p(1 − p) is largest at 50%, giving the most conservative margin; a reported "±3%" is usually based on 50%.
误差范围包括所有误差吗？Does it cover all errors?
不。它只反映随机抽样误差，不包括问卷措辞、无应答、抽样框偏差等系统误差。No. It only reflects random sampling error, not bias from question wording, non-response or the sampling frame.
计算精度如何？How precise are the results?
「误差范围计算器（调查抽样）」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Margin of Error Calculator (Surveys) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「误差范围计算器（调查抽样）」免费吗？需要注册吗？Is the Margin of Error Calculator (Surveys) free? Do I need an account?
「误差范围计算器（调查抽样）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Margin of Error Calculator (Surveys) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.