2. 外语
  3. The standard deviation of n numbers x1, x2, x3…, xnwith mean is equal to , where S is the sum of the squared differences (xi-)2

The standard deviation of n numbers x1, x2, x3…, xnwith mean is equal to , where S is the sum of the squared differences (xi-)2

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问题 The standard deviation of n numbers x1, x2, x3…, xnwith mean is equal to , where S is the sum of the squared differences (xi-)2 for 1≤i≤n. The values in list M are the integers 1, 3, and 5, where 1 occurs k times, 3 occurs once, and 5 occurs k times. If the standard deviation of the values in M is less than 1.95, what is the greatest possible value of k?
选项 A、3
B、5
C、7
D、9
E、11
答案D
解析 若没给标准差公式就无须具体计算，只需定性判断。本题给了公式就需要计算。由于有k个1和k个5，数组M的平均值为3。其方差为＜1.95，解得k＜9.63。由于k为正整数，k最大值为9，故答案为D。
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