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The standard deviation of n numbers x1, x2, x3, …, xn with mean is equal to , where S is the sum of the squared differences (x1
The standard deviation of n numbers x1, x2, x3, …, xn with mean is equal to , where S is the sum of the squared differences (x1
admin
2019-05-11
64
问题
The standard deviation of n numbers x
1
, x
2
, x
3
, …, xn with mean
is equal to
, where S is the sum of the squared differences (x
1
-
)
2
for 1≤i≤n. If the standard deviation of the 4 numbers 5-a, 5, 25, and 25+a is 50, where a>0, what is the value of a?
选项
答案
60
解析
通过观察发现5-a,5,25,25+a这四个数是“对称”的,平均值是15,则根据标准差公式:
200+2(a+10)
2
=10000
(a+10)
2
=4900
a+10=70或-70(舍去)
a=60
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