1955 AMC 12 第 3 题

Question

若一组十个数中的每个数都增加

20

，则原来这十个数的算术平均数：

If each number in a set of ten numbers is increased by

20,

the arithmetic mean (average) of the original ten numbers:

保持不变

remains the same

增加

20

is increased by

20

增加

200

is increased by

200

增加

10

is increased by

10

增加

2

is increased by

2

将这十个数都增加二十，会使它们的和增加

10\cdot20

Increasing all ten entries adds

10\cdot20

to their sum

新的总和仍要除以

10

The new total is still divided by

10

若原来的总和为

S

，则新的总和为

S+10\cdot20

。因此新的平均数为

\frac{S+200}{10}=\frac S{10}+20\text{。}

所以平均数增加了

20

。

因此，正确答案是 B。

If the original sum is

S,

the new sum is

S+10\cdot20.

Hence the new mean is

\frac{S+200}{10}=\frac S{10}+20.

The mean is increased by

20.

Thus, the correct answer is B.

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