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.