An Upper Bound on the Value of the Standard Deviation

This article derives a simple upper bound for the sample standard deviation that could be useful in guarding against gross errors of calculation.     

An Upper Bound on Standard Deviation as a Function of Range

This article disproves a conjecture that the ratio of the maximum standard deviation to the range of a set of data decreases as the number of data points increases. It also provides an alternative and more general approach for examining the standard deviation as a function of the range.     

Standard Deviation for Small Samples

Neater representations for variance are given for small sample sizes, especially for 3 and 4. With these representations, variance can be calculated without a calculator if sample sizes are small and observations are integers, and an upper bound for the standard deviation is immediate. Accessible proofs of lower and upper bounds are presented for a broad spectrum of readers.     

A Visual Model for the Variance and Standard Deviation

This paper shows how the variance and standard deviation can be represented graphically by looking at each squared deviation as a graphical object – in particular, as a square. A series of displays show how the standard deviation is the size of the average square.     

教学艺术研究的背离与回归

教学艺术研究有助于克服教学科学化的偏执,追求教学的审美价值,实现教师与学生的个性发展,提升教学境界。然而,既有的教学艺术研究存在研究目标普通化、研究内容策略化、研究方法经验化、研究表达抽象化等问题,背离了艺术的基本精神与研究旨趣。未来教学艺术研究应凸显教学艺术的个性化、回归教学艺术的情境化、强调教学艺术的创造性、重视教学艺术质性研究。     

对标准差控制图的一点讨论

本文针对现有的国家标准标准差控制图的一些问题,在标准差的统计性质的基础上,讨论三种不同的非对称标准差控制图的势函数,并分别给出其在真实报警率下的上、下控制限系数.     

Variability - Does the standard deviation always measure it adequately?

This article discusses an example where four sets of scores with different patterns of variability have the same standard deviation. It is then shown that different measures of variability lead to different conclusions about which set of scores is most variable.     

A Measure of Relative Dispersion

This paper suggests a measure of dispersion which is invariant with respect to linear transformations and distinguishes between large and small spreads.     

杠杆系数、标准差和标准差系数衡量风险的辨析

用收益增长率来阐述企业收益的不确定性，发现杠杆作用不仅改变了企业收益增长率的波动范围，而且也改变了企业收益增长率的平均水平，每股收益和销售量的增长率有相同的标准差系数，表明杠杆作用没有改变企业收益增长率的相对风险。