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If the median and the range of 1, 3, 3, 3, m are the same, w

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If the median and the range of 1, 3, 3, 3, m are the same, w

by Max@Math Revolution » Wed Apr 13, 2016 5:20 pm
If the median and the range of 1, 3, 3, 3, m are the same, which of the following can be the value of m?

A. -1 B. 0 C. 1 D. 2 E. 3

* A solution will be posted in two days.
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by 800_or_bust » Wed Apr 13, 2016 8:40 pm
Max@Math Revolution wrote:If the median and the range of 1, 3, 3, 3, m are the same, which of the following can be the value of m?

A. -1 B. 0 C. 1 D. 2 E. 3

* A solution will be posted in two days.
Easy Peasy. It's clear that the median of this list of numbers must be 3. But if you missed this visually, you can prove it by first testing the scenario where the median = m. In that case, the numbers ordered numerically are 1,3,m,3,3. Therefore, if m is median, m must equal 3. Now test for m<3 and m>3. If m=2, then the list ordered numerically becomes 1,2,3,3,3 and the median is again 3. If m=4, then the list ordered numerically becomes 1,3,3,3,4 and the median is again 3. So we proved that the median is 3 for all values of m. As an aside, if a single value makes up more than half of the total numbers in a list, that number must be the median (by definition). This is the case here, where 3 of the 5 values are identical.

We are given, from the question, that the median and range are the same. Therefore, the range is 3. the range is the difference between the maximum value in the list and the minimum value. We know then that m must be either the maximum or minimum (because the current range based on the known data is only 2, but we know the actual range is 3). If m is the minimum, m must equal 0 (to produce a range of 3). If m is the maximum, m must equal 4. Therefore, m must equal either 0 or 4. Looking at the answer choices, select choice (B) or 0.
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by Max@Math Revolution » Tue Apr 19, 2016 4:54 am
If the median and the range of 1, 3, 3, 3, m are the same, which of the following can be the value of m?

A. -1
B. 0
C. 1
D. 2
E. 3

==> range=Max-min and median is 3. m=4,0 is possible from 3=4-1=3-0.
However, there is only 0 and the answer is B.
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