AMC10 2001 A

AMC10 2001 A · Q1

AMC10 2001 A · Q1. It mainly tests Averages (mean), Arithmetic misc.

The median of the list $n, n+3, n+4, n+5, n+6, n+8, n+10, n+12, n+15$ is 10. What is the mean?

列表 $n, n+3, n+4, n+5, n+6, n+8, n+10, n+12, n+15$ 的中位数是 10。平均数是多少？

(A) 4 4

(B) 6 6

(D) 10 10

(E) 11 11

Answer

Correct choice: (E)

正确答案：（E）

Solution

The middle number in the 9-number list is $n+6$, which is given as 10. Thus $n = 4$. Add the terms together to get $9n + 63 = 9 \cdot 4 + 63 = 99$. Thus the mean is $99/9 = 11$.

9 个数的列表中，中位数是中间的第 5 个数 $n+6$，给定为 10。因此 $n = 4$。各项之和为 $9n + 63 = 9 \cdot 4 + 63 = 99$。因此平均数是 $99/9 = 11$。

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