Question

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

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 $x?$

$50$

$60$

$75$

$90$

$100$

七个数的和为 $540+x$ 。如果平均数等于 $x$ ，则所以 $540=6x$ ， $x=90$ 。 $\frac{540+x}{7}=x,$

当 $x=90$ 时，排序后的数据为 $40,50,60,90,90,100,200$ 。其中位数是 $90$ ，众数也是 $90$ ，所以符合条件。

所以正确答案是 D。

The sum of the seven data values is $540+x$ . If the mean equals $x$ , then $\frac{540+x}{7}=x,$ so $540=6x$ and $x=90$ .

With $x=90$ , the ordered data set is $40,50,60,90,90,100,200$ . Its median is $90$ , and its mode is also $90$ , so the value works.

Thus, the correct answer is D.