Question

$49$ 个连续整数的和为 $7^5$ 。它们的中位数是多少？

The sum of $49$ consecutive integers is $7^5.$ What is their median?

$7$

$7^2$

$7^3$

$7^4$

$7^5$

一组连续整数的和等于项数乘以平均数，而对连续整数来说，平均数等于中位数。

所以中位数为 $\dfrac{7^5}{49} = \dfrac{7^5}{7^2} = 7^3 = 343.$

所以正确答案是 C。

The sum of a set of consecutive integers equals the number of terms times their mean, and for consecutive integers the mean equals the median.

So the median is $\dfrac{7^5}{49} = \dfrac{7^5}{7^2} = 7^3 = 343.$

Thus, the correct answer is C.