AMC 8 2025 Problem 14
AMC8 2025 年第 14 题
统计与数据图表★★★☆☆
A number is inserted into the list 2 , 6 , 7 , 7 , 28 . The mean is now twice as great as the median. What is ?
在一列数字2、6、7、7、28中插入一个数字N，使得这列数字的平均值是中位数的两倍。请问N是多少？
- A.7
- B.14
- C.20
- D.28
- E.34
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
We see the median is 7. Since the mean is two times as great as the median, the mean must be 7×2 = 14. The sum of the numbers without is 2 + 6 + 7 + 7 + 28 = 8 + 14 + 28 = 50. Using the sum, we then have: . Multiplying both sides by 6, we get: N + 50 = 14×6 = 84, . Edited by anabel.disher The median of the list is 7, so the mean of the new list will be . Since there are 6 numbers in the new list, the sum of the 6 numbers will be . Therefore,
Since the average right now is 10, and the median is 7, we see that must be larger than 10, which means that the median of the 6 resulting numbers should be 7, making the mean of these 14. We can do 2 + 6 + 7 + 7 + 28 + N = 14 * 6 = 84. 50 + N = 84, so = i feel this explanation doesn't make much sense
We try out every option by inserting each number into the list. After trying out each number, we get
We could use answer choices to solve this problem. The sum of the 5 numbers is 50. If you add 7 to the list, 57 is not divisible by 6, therefore it will not work. Same thing applies to 14 and 20. The only possible choices left are 28 and 34. Now you check 28. You see that 28 doesn't work because and 13 is not twice of the median, which is still 7. Therefore, only choice left is
We see that in the list, both 7 s are 3 rd and 4 th. So, no matter what number we plug in, we will have two 7 s in 3 rd and 4 th. So, the median will always be 7. That means we have to find the option that makes the mean 14. If the mean is 14, the sum of all the six numbers is 84. The sum of the five numbers we are given is 50, so the answer must be
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