Question

一个数 $N$ 被插入列表 $2$ 、 $6$ 、 $7$ 、 $7$ 、 $28$ 中。现在平均数是中位数的两倍。 $N$ 是多少？

A number $N$ is inserted into the list $2,$ $6,$ $7,$ $7,$ $28.$ The mean is now twice as great as the median. What is $N?$

$7$

$14$

$20$

$28$

$34$

答案：E

知识点：平均数中位数（数据）

难度评级：1170

视频讲解：

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文字解答：

插入 $N$ 后共有 $6$ 个数。个数为偶数，所以中位数是中间两个数的平均。

所有选项都至少为 $7$ ，所以插入后中间两个数仍是 $7$ 和 $7$ 。方便的是，无论选哪个选项，中位数都是 $7$ 。

平均数是中位数的两倍，即 $2 \times 7 = 14$ 。

要让 $6$ 个数的平均数为 $14$ ，总和必须为 $6 \times 14 = 84$ 。

原来 $5$ 个数的和为所以答案是 $84 - 50 = 34$ ，选 E。 $2 + 6 + 7 + 7 + 28 = 50,$

After inserting $N$ into the list, there will be $6$ total numbers. That is even, so the median will be the average of the middle two numbers.

All of the answer choices are at least $7,$ so when they are inserted into the list, the middle two numbers will be $7$ and $7.$ It is convenient that the median will always be $7,$ no matter which answer choice is picked.

The mean becomes twice the median, which is $2 \times 7 = 14.$

To have a total of $6$ numbers with mean $14,$ their sum must become $6 \times 14 = 84.$

The sum of the original $5$ numbers is $2 + 6 + 7 + 7 + 28 = 50,$ so the answer is $84 - 50 = 34,$ which is choice E.

2025 AMC 8 第 14 题

答案：E

难度评级：1170

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文字解答：

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