SAT One-variable data: distributions and measures of center and spread Practice Question 8 (Hard)

Question bank / One-variable data: distributions and measures of center and spread

Math · Problem-Solving and Data AnalysisHard

A data set consists of the seven values $10, 14, 15, 15, 18, 21,$ and $x$ . If the mean of the data set is equal to its median, what is the value of $x$ ?

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Answer: 12

Of the six known values, four are at most $15$ ( $10, 14, 15, 15$ ) and four are at least $15$ ( $15, 15, 18, 21$ ). So wherever $x$ falls, the $4$ th value in order is $15$ , and the median is $15$ . For the mean to be $15$ , the sum must be $7 \times 15 = 105$ . The known values sum to $93$ , so $x = 105 - 93 = 12$ .

Answering $15$ assumes $x$ must equal the median, but $x = 15$ makes the mean $\frac{108}{7}$ , not $15$ .

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