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| 统计量 | Excel函数 | 计算公式 |
|---|---|---|
| 平均值 | =AVERAGE(range) | \(\bar{x}=\dfrac{1}{n} \sum\limits_{i = 1}^n{x_i}\) |
| 样本方差 | =VAR.S(range) | \(s^2=\dfrac{1}{n-1} \sum\limits_{i = 1}^n \left(x_i-\bar{x}\right)^2=\dfrac{1}{n-1}\left(\sum\limits_{i=1}^n x_i^2-n \bar{x}^2\right)\) |
| 样本标准偏差 | =STDEV.S(range) | \(s = \sqrt{\dfrac{1}{n-1} \sum\limits_{i=1}^{n}(x_i - \bar{x})^2}\) |
| 总体方差 | =VAR.P(range) | \(\sigma^2 = \dfrac{1}{N} \sum\limits_{i=1}^{N}(x_i - \mu)^2\) |
| 总体标准偏差 | =STDEV.P(range) | \(\sigma = \sqrt{\dfrac{1}{N} \sum\limits_{i=1}^{N}(x_i - \mu)^2}\) |
| 相对标准偏差 | =STDEV.S(range)/AVERAGE(range) | \(RSD = \dfrac{s}{\bar{x}} \times 100%\) |
| 平均偏差 | =AVERAGE(range)-AVERAGE(reference_range) | \(AD = \dfrac{1}{n} \sum\limits_{i=1}^{n}(x_i - \bar{x})\) |
| 置信区间 | =AVERAGE(range)-CONFIDENCE.NORM(alpha,STDEV.S(range),COUNT(range))=AVERAGE(range)+CONFIDENCE.NORM(alpha,STDEV.S(range),COUNT(range)) | \(CI = \bar{x} \pm z_{\frac{\alpha}{2}} \dfrac{s}{\sqrt{n}}\) |
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