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题库 / Prep2007E1-DS-113
For a certain set of n numbers, where n > 1, is the average (arithmetic mean) equal to the median?
(1) If the n numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2.
(2) The range of the n numbers in the set is 2(n - 1).
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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1）any successive number指的是相邻的数
2）有可能前n-1个数相同，最后一个不同
any pair of successive numbers 相邻的两个数，也就是等差数列
In any evenly spaced set the mean (average) is equal to the median. Sufficient.
In any evenly spaced set the mean (average) is equal to the median. Sufficient.
等差数列的平均数=中位数，无论个数是奇数个还是偶数个。因为等差数列的a(1)+a(n)=a(2)+a(n-1)=……，如果是奇数个，平均数=头尾相加/2=最中间的数/1=最中间的数=中位数；如果是偶数个，平均数=头尾相加/2=最中间的数相加/2=中位数
一组数字，问他们的平均数=中位数？
条件1: 按大小排序，连续两个的差是2 ，以2为差 的 等差数列，比如 2,4,6 2,4,6,8 平均数=中位数 sufficient
条件2:最大值-最小值=2(n-1) 比如n=3 那么有3个数，比如2,3,6 平均数=5.5 中位数= 3; 比如2,4,6 平均数=中位数=4 insufficient
n的意义是数列里数字的个数。。。忘记了，呃。。。
Any pair of seccessive numbers