Question

Hammie 上 $6$ 年级，体重 $106$ 磅。他的四胞胎妹妹还是小婴儿，体重分别为 $5$ 、 $5$ 、 $6$ 和 $8$ 磅。这五个孩子的平均体重和中位数哪个更大，大多少磅？

Hammie is in the $6$ th grade and weighs $106$ pounds. His quadruplet sisters are tiny babies and weigh $5,$ $5,$ $6,$ and $8$ pounds. Which is greater, the average (mean) weight of these five children or the median weight, and by how many pounds?

$\text{median, by } 60$

$\text{median, by } 20$

$\text{average, by } 5$

$\text{average, by } 15$

$\text{average, by } 20$

答案：E

知识点：平均数中位数（数据）

难度评级：770

视频讲解：

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文字解答：

体重按顺序排列后，中间的值是 $6$ ，所以中位数是六磅。 $\cancel{ 5 },\cancel{ 5 },\underline{6},\cancel{8},\cancel{106}$

平均数为它比中位数大 $20$ 磅。 $\begin{align*} &\dfrac{106 + 5 + 5 + 6 + 8}{5} \\&= \dfrac{130}{5}\\ &= 26. \end{align*}$

平均数更大，所以正确答案是 E。

The median weight is the middle value, which we can find as: $\cancel{ 5 },\cancel{ 5 },\underline{6},\cancel{8},\cancel{106}$ Therefore, the median is $6$ pounds.

The average (mean) can be calculated to be: $\begin{align*} &\dfrac{106 + 5 + 5 + 6 + 8}{5} \\&= \dfrac{130}{5}\\ &= 26. \end{align*}$ This is greater than the median, specifically, the mean is $20$ pounds greater than the median.

Thus, E is the correct answer.

2013 AMC 8 第 5 题

答案：E

难度评级：770

视频讲解：

文字解答：

其他年份的第 5 题