AMC8 1990

AMC8 1990 · Q20

AMC8 1990 · Q20. It mainly tests Averages (mean), Arithmetic misc.

The annual incomes of 1,000 families range from \$8200 to \$98,000. In error, the largest income was entered on the computer as $980,000. The difference between the mean of the incorrect data and the mean of the actual data is

1000 个家庭的年收入从 8200 美元到 98,000 美元。由于输入错误，最高收入在计算机上被输入为 980,000 美元。不正确数据平均数与实际数据平均数的差值为

(A) $882 $882

(B) $980 $980

(D) $482,000 $482,000

(E) $882,000 $882,000

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): The difference between the incorrect sum and the actual sum is $\$980{,}000 - \$98{,}000 = \$882{,}000$. Since this difference is equally shared by all 1000 families, the difference between the means is $\frac{882000}{1000} = \$882$.

答案（A）：错误总和与实际总和之间的差为 $\$980{,}000 - \$98{,}000 = \$882{,}000$。由于这笔差额由 1000 个家庭平均分担，因此两个平均数之间的差为 $\frac{882000}{1000} = \$882$。

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