Chapter 2 位置与离散程度度量

\[ \text{中点} = \frac{\text{组上限} + \text{组下限}}{2} \]

\[ \text{类宽} = \text{上类边界} - \text{下类边界} \]

\[ \bar{x} = \frac{\sum x}{n} \]

\[ \bar{x} = \frac{\sum fx}{\sum f} \]

\[ \bar{x} = \frac{n_1\bar{x}_1 + n_2\bar{x}_2}{n_1 + n_2} \]

\[ \text{位置} = \frac{n + 1}{2} \]

\[ Q_1: \frac{n}{4}, \quad Q_2: \frac{n}{2}, \quad Q_3: \frac{3n}{4} \]

\[ P_p: \frac{p \times n}{100} \]

\[ \text{估计值} = \text{组下限} + \frac{\text{目标位置}-\text{前一组累计频率}}{\text{本组频率}} \times \text{组宽} \]

\[ \text{Range} = \text{最大值} - \text{最小值} \]

\[ \text{IQR} = Q_3 - Q_1 \]

\[ \text{百分位距} = P_{upper} - P_{lower} \]

\[ \sigma^2 = \frac{\sum x^2}{n} - \left( \frac{\sum x}{n} \right)^2 \]

\[ \sigma^2 = \frac{\sum fx^2}{\sum f} - \left( \frac{\sum fx}{\sum f} \right)^2 \]

\[ \sigma = \sqrt{\sigma^2} \]

\[ y = \frac{x - a}{b} \]

\[ \bar{x} = b\bar{y} + a \]

\[ \sigma_x = b\sigma_y \]