Finding the Median from the Mean and Standard Deviation

[cmkluza]

I'm having trouble with the following question:

Consider the set of numbers \(\displaystyle x_1, \dots, x_m, y_1, \dots, y_n\) where \(\displaystyle x_i = 0\) for \(\displaystyle i = 1, \dots, m \) and \(\displaystyle y_i = 1\) for \(\displaystyle i = 1, \dots, n\).

Given that M=S, find the value of the median.

M = Mean = \(\displaystyle \frac{n}{m+n}\)
S = Standard Deviation = \(\displaystyle \frac{\sqrt(mn)}{m+n}\)
S = M \(\displaystyle \rightarrow \frac{n}{m+n} = \frac{\sqrt(mn)}{m+n}\)
\(\displaystyle \therefore n = \sqrt(mn)\)

I'm not sure where to go with this information from here. Can anyone tell me how the mean, the standard deviation, and the median relate?

Any tips or advice will be greatly appreciated, thanks!

 

[Deleted member 4993]

I'm having trouble with the following question:

Consider the set of numbers \(\displaystyle x_1, \dots, x_m, y_1, \dots, y_n\) where \(\displaystyle x_i = 0\) for \(\displaystyle i = 1, \dots, m \) and \(\displaystyle y_i = 1\) for \(\displaystyle i = 1, \dots, n\).

Given that M=S, find the value of the median.

M = Mean = \(\displaystyle \frac{n}{m+n}\)
S = Standard Deviation = \(\displaystyle \frac{\sqrt(mn)}{m+n}\)
S = M \(\displaystyle \rightarrow \frac{n}{m+n} = \frac{\sqrt(mn)}{m+n}\)
\(\displaystyle \therefore n = \sqrt(mn)\) → m = n

I'm not sure where to go with this information from here. Can anyone tell me how the mean, the standard deviation, and the median relate?

Any tips or advice will be greatly appreciated, thanks!

What are your thoughts?

Please share your work with us ...even if you know it is wrong

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[cmkluza]

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

I think the edit you put in the quote cleared it all up for me. Since \(\displaystyle n = m\) then there should be an even number of terms (\(\displaystyle 2n\)) hence, it'll be the middle two terms added together and divided by two. Logically, the answer should be \(\displaystyle \frac{1 + 0}{2} = \frac{1}{2}\). Thanks a bunch for your help!