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2016 AMC 12A Problem 4

Problem 4 of 25EasierAlgebra

The mean, median, and mode of the 77 data values 60,60, 100,100, x,x, 40,40, 50,50, 200,200, 9090 are all equal to x.x. What is the value of x?x?

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Solution

The mean condition gives 60+100+x+40+50+200+907=540+x7=x, \begin{gathered} \small \dfrac{60+100+x+40+50+200+90}{7}\\ =\dfrac{540+x}{7}\\ =x, \end{gathered} so 540+x=7x540+x=7x and x=90.x=90. In nondecreasing order the data are 40,50,60,90,90,100,200,40, 50, 60, 90, 90, 100, 200, so the median is 9090 and the mode is 90,90, as required. Thus, the correct answer is D.

More practice

Concepts: mean · median (data) · mode

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.