AMC12 2016 A

AMC12 2016 A · Q4

AMC12 2016 A · Q4. It mainly tests Averages (mean), Arithmetic misc.

The mean, median, and mode of the 7 data values $60, 100, x, 40, 50, 200, 90$ are all equal to $x$. What is the value of $x$?

7个数据 $60, 100, x, 40, 50, 200, 90$ 的平均数、中位数和众数都等于 $x$。求 $x$ 的值。

(A) 50 50

(B) 60 60

(D) 90 90

(E) 100 100

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): The mean of the data values is $\dfrac{60+100+x+40+50+200+90}{7}=\dfrac{x+540}{7}=x.$ Solving this equation for $x$ gives $x=90$. Thus the data in nondecreasing order are $40,50,60,90,90,100,200$, so the median is $90$ and the mode is $90$, as required.

答案（D）：数据的平均数为 $\dfrac{60+100+x+40+50+200+90}{7}=\dfrac{x+540}{7}=x.$ 解该方程得到 $x=90$。因此，按非递减顺序排列的数据为 $40,50,60,90,90,100,200$，所以中位数是 $90$，众数也是 $90$，符合要求。

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