# 集中趋势

## 集中趨勢的統計量

truncated mean）

midrange）

midhinge）

winsorized mean）

$\frac{\overbrace{x_2 + x_2} + x_3 + x_4 + x_5 + x_6 + x_7 + x_8 + \overbrace{x_9 + x_9}}{10}$

## 平均數、中位數與眾數的關係

$\frac{| \theta - \mu |}{ \sigma } \le \sqrt{ 3 }$
$\frac{| \nu - \mu |}{ \sigma } \le \sqrt{ 0.6 }$
$\frac{| \theta - \nu |}{ \sigma } \le \sqrt{ 3 }$

$\frac{| \nu - \mu |}{ \sigma } \le 1$

## 參考文獻

1. ^ Weisberg H.F (1992) Central Tendency and Variability, Sage University Paper Series on Quantitative Applications in the Social Sciences, ISBN 0-8039-4007-6 p.2
2. ^ Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP for International Statistical Institute. ISBN 0-19-920613-9 (entry for "central tendency")
3. ^ 3.0 3.1 Upton, G.; Cook, I. (2008) Oxford Dictionary of Statistics, OUP ISBN 978-0-19-954145-4 (entry for "central tendency")
4. ^ Johnson NL, Rogers CA (1951) "The moment problem for unimodal distributions". Annals of Mathematical Statistics, 22 (3) 433–439
5. ^ Hotelling H, Solomons LM (1932) The limits of a measure of skewness. Annals Math Stat 3, 141–114
6. ^ Garver (1932) Concerning the limits of a mesuare of skewness. Ann Math Stats 3(4) 141–142