1990 AMC 8 Problem 20

Below is the professionally curated solution for Problem 20 of the 1990 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1990 AMC 8 solutions, or check the answer key.

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Concepts:mean

Difficulty rating: 1060

20.

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

$882

$980

$1078

$482,000

$882,000

Solution:

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

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

Thus, the correct answer is A .

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