Sources — learn-standard-deviation-and-normal-distribution

取材缓存(2026-06-30)。主题定位:统计基础入门,范围限定在离散程度、方差/标准差、样本 vs 总体、正态曲线、经验法则、z-score。

S1 — OpenStax Introductory Statistics 2e: Measures of the Spread of the Data

• URL: https://openstax.org/books/introductory-statistics-2e/pages/2-7-measures-of-the-spread-of-the-data
• 权威: 权威教程/书
• 支撑: spread/range 的定义,离散程度作为数据相隔远近的度量。
• 关键事实摘录: spread describes how far apart data values are; range is maximum minus minimum; standard deviation is a common measure of spread.

S2 — Khan Academy: Variance and standard deviation of a population

• URL: https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data/variance-standard-deviation-population/a/population-standard-deviation
• 权威: 权威教程/书
• 支撑: 总体方差和总体标准差的手算步骤,平方偏差、平均、开方的教学顺序。
• 关键事实摘录: population variance is the mean of squared distances from the mean; population standard deviation is the square root of variance.

S3 — OpenStax Introductory Statistics 2e: Standard Deviation in Measures of the Spread

• URL: https://openstax.org/books/introductory-statistics-2e/pages/2-7-measures-of-the-spread-of-the-data
• 权威: 权威教程/书
• 支撑: 标准差公式、样本标准差常用 n-1、标准差单位与解释。
• 关键事实摘录: standard deviation measures spread around the mean; sample standard deviation uses n-1 in the denominator.

S4 — OpenStax Introductory Statistics 2e: Definitions of Statistics, Probability, and Key Terms

• URL: https://openstax.org/books/introductory-statistics-2e/pages/1-1-definitions-of-statistics-probability-and-key-terms
• 权威: 权威教程/书
• 支撑: population/sample、parameter/statistic 的术语边界。
• 关键事实摘录: a population is the complete group under study; a sample is a subset; a parameter describes a population and a statistic describes a sample.

S5 — NIST/SEMATECH e-Handbook of Statistical Methods: Normal Distribution

• URL: https://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm
• 权威: 官方文档
• 支撑: 正态分布是常用连续分布,由位置和尺度参数刻画,曲线形状与均值/标准差相关。
• 关键事实摘录: the normal distribution is widely used; its probability density depends on location and scale parameters, commonly mean and standard deviation.

S6 — OpenStax Introductory Business Statistics 2e: Using the Normal Distribution

• URL: https://openstax.org/books/introductory-business-statistics-2e/pages/6-2-using-the-normal-distribution
• 权威: 权威教程/书
• 支撑: 正态曲线的对称性、曲线下面积表示概率、经验法则。
• 关键事实摘录: normal distributions are symmetric; probabilities correspond to area under the curve; the empirical rule gives about 68%, 95%, and 99.7%.

S7 — NIST/SEMATECH e-Handbook of Statistical Methods: Standard Normal Distribution

• URL: https://www.itl.nist.gov/div898/handbook/eda/section3/eda3671.htm
• 权威: 官方文档
• 支撑: 标准正态分布平均数 0、标准差 1,z-score 标准化思想。
• 关键事实摘录: the standard normal distribution has mean 0 and standard deviation 1; standardization maps values to this reference distribution.

S8 — Khan Academy: Normal distributions and the empirical rule

• URL: https://www.khanacademy.org/math/statistics-probability/modeling-distributions-of-data/more-on-normal-distributions/a/normal-distributions-and-the-empirical-rule
• 权威: 权威教程/书
• 支撑: 68-95-99.7 经验法则的入门解释和区间估算。
• 关键事实摘录: for normal distributions, about 68% of data are within 1 standard deviation, 95% within 2, and 99.7% within 3.

S9 — Khan Academy: Z-scores review

• URL: https://www.khanacademy.org/math/statistics-probability/modeling-distributions-of-data/z-scores/a/z-scores-review
• 权威: 权威教程/书
• 支撑: z-score 公式、正负号解释、跨分布位置比较。
• 关键事实摘录: a z-score tells how many standard deviations a value is from the mean; positive is above the mean and negative is below.

覆盖核对

1. spread/range/variance/std

• S1 支撑 spread/range; S2/S3 支撑方差与标准差。

2. sample vs population

• S3 支撑样本标准差分母 n-1; S4 支撑总体、样本、参数、统计量术语。

3. normal curve

• S5/S6 支撑正态分布形状、均值、标准差、面积。

4. empirical rule

• S6/S8 支撑 68-95-99.7。

5. z-score

• S7/S9 支撑标准正态与 z-score 解释。