关于连续函数平均值的研究  

Research on the Average Continuous Function

作　　者：王雪琴[1] 杨秀香[1] 

机构地区：[1]渭南师范学院数学与信息科学学院,陕西渭南714099

出　　处：《渭南师范学院学报》2015年第10期22-25,共4页Journal of Weinan Normal University

基　　金：渭南师范学院教育科学研究课题:西方教师教育大学与中小学合作体制特点(2014JYKX021)

摘　　要：平均值概念在统计学中起着非常重要的作用,而定积分的本质是积分和的极限值,也是一种特殊的"和",具有统计的性质.因此从积分中值定理出发,引申出连续函数在区间上平均值的概念,同时研究出该平均值函数相应的基本性质,进而应用这些性质特征求函数的平均值、证明积分不等式等.在证明实例中得出在连续条件下几何平均值小于等于算术平均值的结论,从而扩大了平均值概念的范围.The concept plays in the statistical average of a very important role, and the definite integral is the integral nature and limits, but also a special ＂and＂ statistical in nature. Therefore, from the integral value theorem gives rise to a continuous the concept function on the interval for the mean, while developed the basic nature of the average of the corresponding functions. Further application of these properties feature averaging function, prove integral inequality, etc. come under continuous conditions of geomet？ric mean less arithmetic average of the conclusions in the proof instances, thus expanding the scope of the average value of the con？cept.

关 键 词：连续函数 平均值 统计量 

分 类 号：O174[理学—数学]