2020-I-09

$\begin{array}{cl}=& {\displaystyle \frac{4\times 8+5\times 12+6\times 16+7\times 4}{8+12+16+4}}\\ =& 5.4\end{array}$

由於該班有 $40$ 名學生，所以中位數

$\begin{array}{cl}=& {\displaystyle \frac{\text{第 20 個數據}+\text{第 21 個數據}}{2}}\\ =& {\displaystyle \frac{5+6}{2}}\\ =& 5.5\end{array}$

標準差

$\begin{array}{cl}=& 0.976515139\end{array}$

$\begin{array}{cl}=& \text{第 21 個數據}\\ =& 5\end{array}$

由此，中位數的減少

$\begin{array}{cl}=& 5.5–5\\ =& 0.5\end{array}$