MathDB
Equivalent averages

Source: 2016 AMC 10A #7

February 3, 2016
AMCAMC 10AMC 10 A2016 AMC 10Aarithmetic meanmodemedian

Problem Statement

The mean, median, and mode of the 77 data values 60,100,x,40,50,200,9060, 100, x, 40, 50, 200, 90 are all equal to xx. What is the value of xx?
<spanclass=′latex−bold′>(A)</span> 50<spanclass=′latex−bold′>(B)</span> 60<spanclass=′latex−bold′>(C)</span> 75<spanclass=′latex−bold′>(D)</span> 90<spanclass=′latex−bold′>(E)</span> 100<span class='latex-bold'>(A)</span>\ 50 \qquad<span class='latex-bold'>(B)</span>\ 60 \qquad<span class='latex-bold'>(C)</span>\ 75 \qquad<span class='latex-bold'>(D)</span>\ 90 \qquad<span class='latex-bold'>(E)</span>\ 100
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