GMAT数学精解--算术概述(3)

文章作者 100test 发表时间 2007:03:25 21:43:47
来源 100Test.Com百考试题网

八.描述统计(DESCRIPTIVE STATISTICS)

　　1.平均数(AVERAGE OR ARITHMETIC MEAN)

　　2.中数(MEDIAN)

　　TO CALCULATE THE MEDIAN OF N NUMBERS，FIRSTSGROUPSTHE NUMBERS FROM LEAST TO GREATEST；IF N IS ODD，THE MEDIAN IS DEFINED AS THE MIDDLE NUMBER，WHILE IF N IS EVEN，THE MEDIAN IS DEFINED AS THE AVERAGE OF THE TWO MIDDLE NUMBERS. FOR THE DATA 6, 4, 7, 10, 4, THE NUMBERS, IN ORDER, ARE 4, 4, 6, 7, 10, AND THE MEDIAN IS 6, THE MIDDLE NUMBER. FOR THE NUMBERS 4, 6, 6, 8, 9, 12, THE MEDIAN IS (6 8 )/2 = 7. NOTE THAT THE MEAN OF THESE NUMBERS IS 7.5.

　　3.众数(MODE)：一组数中的众数是指出现频率最高的数。

　　例：THE MODE OF 7，9，6，7，2，1 IS 7。

　　4.值域(RANGE)：表明数的分布的量，其被定义为最大值减最小值的差。

　　例：THE RANGE OF–1，7，27，27，36 IS 36-(-1)= 37。

　　5.标准方差(STANDARD DEVIATION)：

　　ONE OF THE MOST COMMON MEASURES OF DISPERSION IS THE STANDARD DEVIATION. GENERALLY SPEAKING, THE GREATER THE DATA ARE SPREAD AWAY FROM THE MEAN, THE GREATER THE STANDARD DEVIATION. THE STANDARD DEVIATION OF N NUMBERS CAN BE CALCULATED AS FOLLOWS:

　　(1)FIND THE ARITHMETIC MEAN .

　　(2)FIND THE DIFFERENCES BETWEEN THE MEAN AND EACH OF THE N NUMBERS .

　　(3)SQUARE EACH OF THE DIFFERENCES .

　　(4)FIND THE AVERAGE OF THE SQUARED DIFFERENCES .

　　(5)TAKE THE NONNEGATIVE SQUARE ROOT OF THIS AVERAGE.

　　NOTICE THAT THE STANDARD DEVIATION DEPENDS ON EVERY DATA VALUE, ALTHOUGH IT DEPENDS MOST ON VALUES THAT ARE FARTHEST FROM THE MEAN. THIS IS WHY A DISTRIBUTION WITH DATA GROUPED CLOSELY AROUND THE MEAN WILL HAVE A SMALLER STANDARD DEVIATION THAN DATA SPREAD FAR FROM THE MEAN.