The frequency table summarizes a data set, where k is a... | SAT One-variable data: distributions and measures of center and spread Question, Answer Explained

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

Math · Problem-Solving and Data AnalysisHard

Value	Frequency
1	4
2	6
3	$k$
4	3

The frequency table summarizes a data set, where $k$ is a positive integer. If the median of the data set is $3$ , what is the least possible value of $k$ ?

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Answer: 8

There are $4 + 6 = 10$ values less than $3$ , and the data set has $13 + k$ values in all. If $k = 7$ , there are $20$ values, and the median is the average of the $10$ th value, $2$ , and the $11$ th value, $3$ , which is $2.5$ . If $k = 8$ , there are $21$ values, and the median is the $11$ th value, which is $3$ . So the least possible value of $k$ is $8$ .

With $k = 7$ , exactly half of the $20$ values are less than $3$ , so the median is $2.5$ , not $3$ .

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