BMJ小小統計問題（4）：離散程度測量指標

前言

British Medical Journal，英國醫學期刊（簡稱 BMJ），創始於1840年，在醫學研究領域享有盛名。本系列匯東華精選BMJ所發行之3百多題Statistical Question，採用中英對照有興趣的朋友們可進行回答。各題都有詳細說明。

完整合輯請見官網／學習專區／BMJ小小統計問題

問題

BMJ 統計問題（4）：下列何者為離散程度測量指標？

Which, if any, of the following are measures of spread?

1. Mode（眾數）
2. Interquartile range（四分位差）
3. Skewness（偏度）
4. Variance（變異數）

答案

答案是 b) Interquartile range（四分位差）以及 d) Variance（變異數）

詳細說明

在呈現數值類型的資料時，給出數值所含括的範圍是很有用的。最大值與最小值將定義整個範圍，但無法描繪含括數值的典型程度。離散指標提供觀察值分散情形的摘要。

When presenting numerical data it is useful to give an idea of the range of values covered by the data. The maximum and minimum values would define the entire range, but would not describe how typical these values would be. Measures of spread provide a summary of how spread out observations typically are.

四分位差為描述包括中間50%數值的範圍區間。25%低於此範圍，以及25%高於此範圍。

The interquartile range is described by the bottom and top values that contain the middle 50% of the observations in the set of data. 25% of observations fall below this range and 25% above it.

變異數是所有觀察值與平均值差異平方之總和平均數（均方），開根號即為標準差。

Variance is the average of the square of all the differences between individual observations and the mean. Taking the square root of this gives the familiar standard deviation.

眾數是一組數據中出現頻率最高的值，而非測量離散程度。

The mode is the most frequent value in a set of data and does not measure spread.

偏度是測量一組數據缺乏對稱的偏斜程度，而非測量離散程度。

Skewness is a measure of the lack of symmetry in a set of data and does not measure spread.

參考文獻

1.  改編自：BMJ Statistical Question