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Shows the number of children per family for 50 families in a housing estate

\begin{array}{cc} \textrm{No. of Children} &\textrm{No. Of Families} \\ 0& 4\\ 1& m\\ 2& n\\ 3& 8\\ 4& 4\\ 5& 2\\ \end{array} If MIN is 2, find m and n.

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    please, add homework to your homework questions, and use LaTeX to add style2012-08-30

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Here is a wild guess about the information we are given. I will assume that when you write that MIN is $2$, you mean that the mean number of children per family is $2$.

There are $50$ families. But we can see by adding up the entries in the column on the right that there are $18+m+n$ families. So $50=18+m+n$, and therefore $m+n=32$.

The mean number of children per family is $2$. The mean is the total number of children divided by the number of families. So if $T$ is the total number of children, then $\frac{T}{50}=2$, meaning that $T=100$.

But from the table, $T=(0)(4)+(1)(m)+(2)(n)+(3)(8)+(4)(4)+(5)(2).$ Simplify. We find that $T=50+m+2n$. But $T=100$, so $50+m+2n=100$ and therefore $m+2n=50$.

We now have the two linear equations $m+n=32$ and $m+2n=50$. By subtraction, we find that $n=(m+2n)-(m+n)=50-32=18$.

But then since $m+n=32$, we have $m=14$.