QCSunny Lab

Descriptive Statistics描述统计与线性回归

Paste a list of numbers — separated by spaces, commas, semicolons or new lines — and get the full statistics at once: mean, median, mode, sum, count, min, max, and both sample and population standard deviation.

The mean is the sum divided by the count; the median is the middle value (robust to outliers); the mode is the most frequent value. Invalid entries are ignored and listed so you can fix them. Optionally paste an equally long x list and the calculator also fits the regression line y = a + b·x by least squares.

Frequently asked questions

Mean or median — which should I use?

The median when the data has outliers or is skewed (like incomes); the mean is fine for symmetric data.

What is the difference between the two standard deviations?

Sample (s) divides by n−1 for estimating from a sample; population (σ) divides by n when you have every value.

What if no number repeats?

Then there is no mode, and the calculator shows "—".

What does the regression line tell me?

It fits y = a + b·x to your (x, y) pairs: b is the slope and a the intercept, both shown when you provide equally long x and y lists.

中文说明

粘贴一组数字(支持空格、逗号、分号或换行分隔),一次性得到完整统计:均值、中位数、众数、总和、个数、最值,以及样本与总体两种标准差。

均值 = 总和 ÷ 个数;中位数是排序后的中间值(对异常值稳健);众数是出现最频繁的值。无法解析的条目会被忽略并列出,便于修正。若再粘贴一组等长 x 数值,还会以最小二乘拟合回归直线 y = a + b·x。

常见问题

均值和中位数用哪个?

数据有异常值或偏态(如收入)时用中位数;对称分布的数据用均值即可。

两种标准差有什么区别?

样本标准差(s)除以 n−1,用于从样本估计;总体标准差(σ)除以 n,适用于拥有全部数据的情形。

如果没有数字重复怎么办?

那就没有众数,计算器会显示"—"。

回归直线表示什么?

以最小二乘对每组 (x, y) 拟合 y = a + b·x:b 为斜率、a 为截距。当 x 与 y 等长时自动计算显示。