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176 lines
7.9 KiB
HTML
176 lines
7.9 KiB
HTML
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<head>
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<title>Accuracy and Precision</title>
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<meta name="description" content="Accuracy and Precision mean slightly different things!" />
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<div id="content" role="main"><!-- #BeginEditable "Body" -->
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<h1 align="center">Accuracy and Precision</h1>
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<p class="center"><i>They mean slightly different things!</i>
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</p>
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<h2>Accuracy</h2>
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<p align="center">Accuracy is how close a measured value is to the <b>actual (true) value</b>.
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</p>
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<h2>Precision</h2>
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<p align="center">Precision is how close the measured values are <b>to each other</b>.
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</p>
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<h2>Examples</h2>
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<h3>Here is an example of several values on the <a href="number-line.html">number line</a>:</h3>
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<p class="center"><img src="data/images/accuracy-precision.svg" alt="accuracy and precision" /></p>
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<h3>And an example on a Target:</h3>
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<div class="simple">
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<table border="0" cellspacing="5" align="center">
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<tr align="center">
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<td><img src="images/hi-accuracy-low-precision.svg" alt="hi accuracy low precision" /></td>
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<td><img src="images/low-accuracy-hi-precision.svg" alt="low accuracy hi precision" /></td>
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<td><img src="images/hi-accuracy-hi-precision.svg" alt="hi accuracy hi precision" /></td>
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</tr>
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<tr align="center">
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<td><b>High Accuracy</b><br />
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Low Precision</td>
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<td>
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Low Accuracy<br />
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<b>High Precision
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</b></td>
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<td><b>High Accuracy<br />
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High Precision
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</b></td>
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</tr>
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</table>
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</div>
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<div class="example">
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<h3>Example: Hitting the Post</h3>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/soccer-teams.jpg" width="209" height="86" alt="soccer goal"></p>
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<p>If you are playing football and you always hit the right goal post instead of scoring, then you are <b>not</b> accurate, but you <b>are</b> precise!</p>
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</div>
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<h2>How to Remember?</h2>
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<ul>
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<li>a<b>C</b>curate is <b>C</b>orrect (a bullseye).</li>
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<li>p<b>R</b>ecise is <b>R</b>epeating (hitting the same spot, but maybe not the correct spot)</li>
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</ul>
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<h2>Bias (don't let precision fool you!)</h2>
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<p>When we measure something several times and all values are close, they <b>may</b> all be wrong if there is a "<b>Bias</b>"</p>
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<p><b>Bias</b> is a systematic (built-in) error which makes all measurements wrong by a certain amount.</p>
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<h3>Examples of Bias</h3>
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<ul>
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<li>The scales read "1 kg" when there is nothing on them</li>
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<li>You always measure your height wearing shoes with thick soles.</li>
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<li>A stopwatch that takes half a second to stop when clicked</li>
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</ul>
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<p>In each case <b>all</b> measurements are wrong by the same amount. That is bias.</p>
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<h2>Degree of Accuracy</h2>
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<p>Degree of Accuracy depends on the instrument we are measuring with. But as a general rule:</p>
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<div class="def">
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<p>The Degree of Accuracy is <b>half a unit</b> each side of the unit of measure.</p>
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</div>
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<h3>Examples:</h3>
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<div class="simple">
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<table border="0" align="center">
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<tr align="center">
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<td>When an instrument measures in "1"s <br />
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any value between <b>6½</b> and <b>7½</b> is measured as <b>"7"</b></td>
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<td><img src="images/accuracy-1.svg" alt="7 plus minus 0.5" /></td>
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</tr>
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<tr align="center">
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<td>When an instrument measures in "2"s <br />
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any value between <b>7</b> and <b>9</b> is measured as <b>"8"</b></td>
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<td><img src="images/accuracy-2.svg" alt="8 plus minus 1" /></td>
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</tr>
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</table>
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</div>
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<p class="center"><i>(Notice that the arrow points to the same spot, but the measured values are different!<br />
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Read more at <a href="measure/error-measurement.html">Errors in Measurement</a>.
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)</i></p>
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<p> </p>
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<p>We should show final values that match the accuracy of our <b>least</b> accurate value used.</p>
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<div class="example">
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/art/sage-looking-ear-down.gif" width="77" height="100" alt="dog"></p>
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<h3>Example: We are told the dog is about 2 feet high. </h3>
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<p>We can convert that to 609.6 mm, but that suggests we know the height to within 0.1 mm! </p>
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<p>So we should use <b>600 mm</b></p>
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</div>
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<p> </p>
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<div class="questions">
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<script type="text/javascript">getQ(5000, 1872, 1873, 1874, 1875, 3788, 3789, 3790, 3791, 5001);</script>
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</div>
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<div class="related"><a href="measure/error-measurement.html">Errors in Measurement
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</a> <a href="data/standard-deviation.html">Standard Deviation and Variance</a> <a href="length-conversion.html">How to Convert Lengths</a>
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<a href="area-conversion.html">How to Convert Areas</a>
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<a href="volume-conversion.html">How to Convert Volumes</a>
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<a href="temperature-conversion.html">Converting Temperatures (Celsius and Fahrenheit)</a> <a href="unit-conversion-tool.html">Unit Converter</a>
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<a href="data/index.html">Probability and Statistics Index</a></div>
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Copyright © 2017 MathsIsFun.com
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