Question

汉米上 $6$ 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?

中位数，大 $60$ 磅

median, by $60$

中位数，大 $20$ 磅

median, by $20$

平均数，大 $5$ 磅

average, by $5$

平均数，大 $15$ 磅

average, by $15$

平均数，大 $20$ 磅

average, by $20$

答案：E

知识点：平均数中位数（数据）

难度评级：770

小提示：

先把五个体重排序，再找中位数

Order the five weights before finding the median.

大提示：

将中位数与总体重除以 $5$ 比较

Compare the median with the total weight divided by $5$ .

视频讲解：

Click to load, then click again to play

文字解答：

体重的中位数就是排序后正中间的那个值，可以这样找出： $\cancel{ 5 },\cancel{ 5 },\underline{6},\cancel{8},\cancel{106}$ 因此中位数是 $6$ 磅。

平均数可以计算如下： $\begin{align*} &\dfrac{106 + 5 + 5 + 6 + 8}{5} \\&= \dfrac{130}{5}\\ &= 26\text{。} \end{align*}$ 这个值比中位数大，具体来说，平均数比中位数大 $20$ 磅。

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