1963 AMC 12 第 11 题

Question

一组

50

个数的算术平均数是

38

。若从中去掉

45

和

55

这两个数，剩余各数的算术平均数是：

The arithmetic mean of a set of

50

numbers is

38.

If two numbers of the set, namely

45

and

55,

are discarded, the arithmetic mean of the remaining set of numbers is:

38.5

37.5

37

36.5

36

根据平均数求出原来的总和

Recover the original sum from the mean

减去

45+55

，再除以

48

Subtract

45+55

and divide by

48

原来的总和是

50\cdot38=1900

。去掉

45+55=100

后，剩余各数之和为

1800

，所以新的平均数为

\frac{1800}{48}=37.5

。

所以正确答案是 B。

The original sum is

50\cdot38=1900.

After removing

45+55=100,

the remaining sum is

1800,

so the new mean is

\frac{1800}{48}=37.5.

Thus, the correct answer is B.

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