2022 AMC 8 第 19 题
先试着解答 2022 AMC 8 第 19 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2022 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
19.
Ramos 老师给 名学生进行了一次测试。下面的点图显示了成绩分布。
后来 Ramos 老师发现某题评分有误。他重新评分，给一些学生额外加了 分，使得测试成绩的中位数提高到 。至少有多少名学生得到了额外分数？
（注意，中位数等于中间 个成绩的平均数；这里 个成绩按从小到大排列。）
Mr. Ramos gave a test to his class of students. The dot plot below shows the distribution of test scores.
Later Mr. Ramos discovered that there was a scoring error on one of the questions. He regraded the tests, awarding some of the students extra points, which increased the median test score to What is the minimum number of students who received extra points?
(Note that the median test score equals the average of the scores in the middle if the test scores are arranged in increasing order.)
小提示：
中位数由第 个和第 个成绩决定
The median is controlled by the th and th scores
大提示：
重新评分前后，数一数至少为 的成绩有多少个
Count how many scores are at least before and after regrading
解答：
所有成绩都是 的倍数，加上 分后仍然如此。如果第 和第 个成绩的平均数是 ，但两者不都是 ，那么第 个成绩至少为 。这就要求至少有 个成绩不低于 。
可是重新评分后，只有原来不低于 的成绩才可能达到 。点图中这样的成绩只有 个，所以中间两个成绩必须都是 。
点图中原来有 个不低于 的成绩。要使第 和第 个成绩都为 ，至少要有 个成绩不低于 。把四个 分提高到 分既是必要的，也是充分的。
所以正确答案是 C。
All scores are multiples of and adding preserves that fact. If the th and th scores average but are not both then the th score must be at least That would require at least scores of or more.
However, even after regrading, only the original scores of or more can reach The plot has only such scores, so the two middle scores must both be
The plot initially has scores of at least To make the th and th scores both there must be at least scores of at least Raising four of the ’s to is both necessary and sufficient.
Thus, the correct answer is C.
其他年份的第 19 题
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