2016 AMC 10A Problem 7

Question

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

Use the mean condition first

After finding

x

, check that median and mode also equal

x

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.

Problem 7 in other years