The following formulas will be provided on the the exam \[\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i, \ \ \bar{x} = \frac{1}{n}\sum_{x} xF(x), \ \ \bar{x} = \sum_{x} xRF(X)\]

\[s^2 = \frac{1}{n-1}\sum_{i=1}^n (x_i - \bar{x})^2, \ \ s = \sqrt{\frac{1}{n-1}\sum_{i=1}^n (x_i - \bar{x})^2}\]

\[ \text{range}(x) = \text{min}(x) - \text{max}(x), \ \ IQR = Q3 - Q1 \]

\[x < Q1 - 1.5 \times (Q3 - Q1), \ \ x > Q3 - 1.5\times(Q3-Q1)\]