1990 AMC 8 第 20 题

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20.

1,0001{,}000 个家庭的年收入从 $8200 到 $98000 不等。由于错误,最高收入在电脑中被输入为 $980000。错误数据的平均数与实际数据的平均数相差多少?

The annual incomes of 1,0001{,}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

$882

$980

$1078

$482000

$482,000

$882000

$882,000

答案:A
知识点:平均数
难度评级:1060
解答:

只有一个数据被改错。错误总和比实际总和多 $980,000$98,000=$882,000\$980{,}000 - \$98{,}000 = \$882{,}000

这多出的金额分摊到 10001000 个家庭上,平均数相差 $882,0001000=$882\dfrac{\$882{,}000}{1000} = \$882

所以正确答案是 A

Only one entry changed. The incorrect total exceeds the actual total by $980,000$98,000=$882,000.\$980{,}000 - \$98{,}000 = \$882{,}000.

Since this extra amount is spread over 10001000 families, the means differ by $882,0001000=$882.\dfrac{\$882{,}000}{1000} = \$882.

Thus, the correct answer is B .

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