🔔 经验法则（68-95-99.7）计算器Empirical Rule Calculator (68-95-99.7)
输入正态分布的平均值和标准差，给出平均值 ±1、±2、±3 个标准差的区间，以及各区间内数据所占的比例（约 68%、95%、99.7%），还可以查某个数值的 z 分数。Enter the mean and standard deviation of a normal distribution to get the ranges within ±1, ±2 and ±3 standard deviations and the share of data in each (about 68%, 95% and 99.7%), plus the z-score of any value.
使用说明与常见问题How-to & FAQ
「经验法则（68-95-99.7）计算器」是什么？What is the Empirical Rule Calculator (68-95-99.7) tool?
输入正态分布的平均值和标准差，给出平均值 ±1、±2、±3 个标准差的区间，以及各区间内数据所占的比例（约 68%、95%、99.7%），还可以查某个数值的 z 分数。Enter the mean and standard deviation of a normal distribution to get the ranges within ±1, ±2 and ±3 standard deviations and the share of data in each (about 68%, 95% and 99.7%), plus the z-score of any value.
如何使用「经验法则（68-95-99.7）计算器」？How do I use the Empirical Rule Calculator (68-95-99.7) tool?
在「经验法则（68-95-99.7）计算器」中，填写「平均值 μ」、「标准差 σ」、「查询数值 x（可选）」等参数，结果会随输入实时计算并显示在下方。In the Empirical Rule Calculator (68-95-99.7): Fill in "Mean μ", "Standard deviation σ", "Value x to look up (optional)"; results are recalculated instantly as you type.
经验法则是什么？What is the empirical rule?
对正态分布，约 68% 的数据落在平均值 ±1 个标准差内，约 95% 在 ±2 个内，约 99.7% 在 ±3 个内。精确值为 68.27%、95.45%、99.73%。For a normal distribution about 68% of values lie within one standard deviation of the mean, about 95% within two and about 99.7% within three. The exact figures are 68.27%, 95.45% and 99.73%.
数据不是正态分布怎么办？What if my data are not normal?
经验法则只适用于近似正态（钟形、对称）的数据。对任意分布可以用切比雪夫不等式：至少 1 − 1/k² 的数据在 ±kσ 内（k = 2 时至少 75%）。The rule only holds for roughly normal (bell-shaped, symmetric) data. For any distribution, Chebyshev's inequality guarantees at least 1 − 1/k² within ±kσ (at least 75% for k = 2).
计算精度如何？How precise are the results?
「经验法则（68-95-99.7）计算器」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 Empirical Rule Calculator (68-95-99.7) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「经验法则（68-95-99.7）计算器」免费吗？需要注册吗？Is the Empirical Rule Calculator (68-95-99.7) free? Do I need an account?
「经验法则（68-95-99.7）计算器」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 Empirical Rule Calculator (68-95-99.7) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.