AMC8 2013

AMC8 2013 · Q5

AMC8 2013 · Q5. It mainly tests Averages (mean), Arithmetic misc.

Hammie is in the 6th 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?

Hammie 在六年级，重 106 磅。他的四胞胎姐妹是小婴儿，重 5、5、6 和 8 磅。这五个孩子的平均体重（均值）还是中位数体重更大，相差多少磅？

(A) median, by 60 中位数，大 60

(B) median, by 20 中位数，大 20

(D) average, by 15 平均，大 15

(E) average, by 20 平均，大 20

Answer

Correct choice: (E)

正确答案：（E）

Solution

Listing the elements from least to greatest, we have $(5, 5, 6, 8, 106)$, we see that the median weight is 6 pounds. The average weight of the five kids is $\frac{5+5+6+8+106}{5} = \frac{130}{5} = 26$. Hence,\[26-6=\boxed{\textbf{(E)}\ \text{average, by 20}}.\]

将元素从小到大排列，我们有 $(5, 5, 6, 8, 106)$，可见中位数体重是 6 磅。五个孩子的平均体重是 $\frac{5+5+6+8+106}{5} = \frac{130}{5} = 26$ 磅。因此，\[26-6=\boxed{\textbf{(E)}\ \text{average, by 20}}.\]

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