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I have a small problem where I am stuck:

I have values which describe a distribution. In particular I have the lower percentiles from $25.5\% - 50\% = 30 - 55$ and the upper percentile $50\% - 97.5\% = 55 - 83$.

I would like to construct two rectangles who have the same overall area, but are fixed in their height: Rectangle 1 ($r_1$) is $25$ units high and $r_2$ is $28$ units high.

Therefore the width should vary. In this case $r_2$ should be somewhat smaller than $r_1$ because it's higher than $r_1$.

To say it another way: $A(r_1) = A(r_2)$ while the height of both rectangles cannot be changed.

grg
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Christian Sauer
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  • Writing it as equation $A = w_1 h = w_2 h$ you see that the widths must be equal, if the area $A$ and the height $h$ both stay the same for both rectangles. However I might interpret "fixed in their height to the Distribution" wrong and you really mean $A = w_1 h_1 = w_2 h_2$ with given $h_1$, $h_2$. Then you should choose $w_1 : w_2 = h_2 : h_1$. Or if you know $A$ use $w_i = A/ h_i$. – mvw Feb 12 '15 at 10:17
  • @mvw Your second equation Looks like my Problem. Thank you. Might you post this? – Christian Sauer Feb 12 '15 at 10:38
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    Nah. It would be nice if you edit your question to make clear that the heights are not constant but in some way relate to the values of your distribution. (That is how I understand it now from your comment) – mvw Feb 12 '15 at 10:47

1 Answers1

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I'm not sure that I understood your question well... Anyway, let $l,w>0$ be respectively the length and width of a rectangle. Let us write $A$, its area.

  • If you know $l$ and $w$, then $A = l \cdot w$.

  • If you know $A$ and $l$, then $w = \frac{A}{l}$.

  • If you know $A$ and $w$, then $l = \frac{A}{w}$.

Surb
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