标准脱差计算器
计算抽样或人口标准差、差异和平均值。
输入结果时更新 。
关于此计算器
Standard deviation measures how spread out a data set is around its mean: a small value means the numbers cluster tightly near the average, a large one means they are widely scattered. This calculator computes both the sample standard deviation (dividing the sum of squared deviations by n − 1, Bessel’s correction) and the population standard deviation (dividing by n), and reports the variance, mean, range and the sum of squared deviations it used. Choose sample when your numbers are a subset drawn from a larger group, and population when they are the entire group.
The method has four steps: find the mean, subtract it from each value to get the deviations, square those deviations and add them up, then divide by n − 1 (sample) or n (population) and take the square root. The square root returns the answer to the same units as the original data, which is why standard deviation is usually preferred over variance for interpretation.
Worked example: for 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5. The squared deviations sum to 32, so the population variance is 32 ÷ 8 = 4 and the population standard deviation is √4 = 2; the sample version divides 32 by 7, giving about 4.57 and a standard deviation of roughly 2.14. The deviation table below shows each value’s distance from the mean and its squared deviation so you can follow the calculation.
经常问到的问题
抽样和人口标准差之间有什么区别?
人口公式将总和平差除以n;抽样公式除以 n- 1. 样本公式除以 n-1(贝塞尔校正)弥补了这样一个事实,即抽样往往低估了它所来自的人口的真正分布。
为什么偏差是平的?
平方根使每个偏差都呈正向, 以免取消, 且偏差的重重更大。 将平方根取底返回到数据原单位 。
我如何用手计算标准偏离?
查找平均值, 从每个值中减去它, 以获得偏差, 平方每个偏差并加起来, 然后在样本中除以 n - 1 或人口为 n, 然后从结果的平方根中取出 。
什么是良好的标准偏离?
不存在普遍“良好”价值——它完全取决于你的数据的规模和背景。标准差仅比平均值有意义;房价的差幅对于测试分可能很大。变差系数表示它为比较平均值的百分比。
标准偏差是零还是负?
它可以是零, 只有当每个值相同, 并且根本没有扩散时才会发生。 它不可能是负的, 因为它是平方数字平均值的平方根 。
为什么样本计算需要至少两个数值?
样本公式除以 n - 1 。 所以单个值会除以零, 并且没有定义。 样本标准差只有在您有两种或两种以上观测可以比较时才有意义 。
API - 使用代码中的计算器
将此计算器称为自由 JSON 端点 。 不需要按键 。 将字段值发送到下面作为查询参数或 JSON 。 任何您省略的, 都会使用相同的默认值, 此页面预填的默认值是预填的; 未知参数是 400, 而不是静音零 。 读取 API 全部文件 →
终点
GET https://calculator.free/api/v1/standard-deviation/curl
curl "https://calculator.free/api/v1/standard-deviation/?numbers=9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4&type=sample"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/standard-deviation/?" + new URLSearchParams({
"numbers": "9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4",
"type": "sample"
}));
const data = await r.json();
console.log(data.results);成果仅是一般指导的估计数,而不是财务、医疗或税务咨询。