Comparing Mean and Median

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If k is the average (arithmetic mean) of the first 8 positive multiples of 6 greater than 6, and if p is the median of the first 8 positive multiples of 6 greater than 6, what is the value of ?

Review: Comparing Mean and Median


Explanation

We can exhaustively enumerate what we are talking about here: the first 8 positive multiples of 6 greater than 6 are: {12, 18, 24, 30, 36, 42, 48, 54}. Their median is the average of the middle two, so it's 33. And moving out from 30 and 36, the numbers are evenly spaced from 33 in pairs. For example, , and , so the first and the last cancel in pulling the average "left" or "right" of 33. Therefore, the median and the mean are both 33, and the ratio of one to the other is 1.

The correct answer is (B).


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