95 lines
2.8 KiB
XML
95 lines
2.8 KiB
XML
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<?xml version="1.0" encoding="ISO-8859-1"?>
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<!--
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Copyright (C) 2015 LoVullo Associates, Inc.
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This file is part of tame-core.
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tame-core is free software: you can redistribute it and/or modify it
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under the terms of the GNU Lesser General Public License as
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published by the Free Software Foundation, either version 3 of the
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License, or (at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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-->
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<package xmlns="http://www.lovullo.com/rater"
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xmlns:c="http://www.lovullo.com/calc"
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xmlns:t="http://www.lovullo.com/rater/apply-template"
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core="true"
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desc="Percentage arithmetic">
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<import package="../base" />
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Converting between real and~percent is trivial:
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$$
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\begin{align}
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r &= p\over100;
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p &= 100r.
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\end{align}
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$$
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^[Percent difference] (also called ^[relative change]) describes
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the~change in value as a~percentage (for example: $10$~is $50%$
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of~$20$, and is~$100%$ of~$5$). ^[Percent change] recognizes the
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direction of the change (that is---$10$ is~$20$ reduced by~$50%$, so
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$p=-50$).
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Since ``change'' sounds like a~verb eclarative contexts, we use
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the~term ^[percent difference] to mean ^[relative change]; it is
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defined as:
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$$\delta \over x = {{x_\beta - x_\alpha}\over{x_\alpha}} \times 100 = p.$$
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Notice that this preserves the direction of the change. So, in the
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context of the previous example, we can say that $10$
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\emph{reduces}~$20$ by~$50%$, giving~$p=-50%$.
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<template name="_rtop_"
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desc="Rational number to percentage">
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<param name="@name@" desc="Percentage to convert" />
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<param name="@index@" desc="Index">
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<text></text>
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</param>
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<param name="@desc@" desc="Optional description">
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<text>Real number to convert into percentage</text>
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</param>
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<param name="@difference@"
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desc="Whether to interpret as a percent difference (default
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false)">
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<text>false</text>
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</param>
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<!-- TODO -->
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<param name="@negate@" desc="Whether to negate percentage before
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conversion">
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<text>false</text>
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</param>
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<c:product>
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<c:sum>
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<c:value-of name="@name@" index="@index@" />
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<if name="@difference@" eq="true">
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<c:const value="-1"
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desc="Percent difference is relative (1 = 100%)" />
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</if>
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</c:sum>
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<c:const value="100"
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desc="Real to percentage" />
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</c:product>
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</template>
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</package>
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