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										<sp count="4"/>DESCRIPTIVE STATISTICS</link>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Multivariate data, or large data sets, may require more sophisticated, nonstatistical visualization just to know which statistics and axes are relevant. Mathcad's surface, scatter, and contour plotting tools and picture operator may help to explore your data. These choices are available from the <f family="Verdana" charset="0">
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					</f> function takes the name of the function you wish to plot, low and high endpoints on the values of two parameters, and the number of steps in each direction. In this case, we're plotting from -2 to 2 over the parameters x2 and x7, and generating 40 data points in each direction.</p>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Two different options for the same contour plot are shown. All settings are controlled by double-clicking on the plot and changing settings on the Appearance and Special tabs. Examine the effect of other variables in the model by changing them in the <f family="Verdana" charset="0">
						<b>
							<inlineAttr line-through="false">
								<c val="#000">Param2</c>
							</inlineAttr>
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					</f> definition.</p>
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				<p style="subsubtitle" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Scatter plots </p>
			</text>
			<indexes>
				<phrase>scatter plots</phrase>
				<phrase>plots, scatter</phrase>
			</indexes>
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			<text use-page-width="false" push-down="false" lock-width="true">
				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Scatter plots can be made in much the same way, with similar options. Note that to pass in the three data vectors representing x, y, and z coordinates, you must group them in parentheses.</p>
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						<ml:str xml:space="preserve">reyesdata.txt</ml:str>
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				<p style="subsubtitle" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Pictures </p>
			</text>
			<indexes>
				<phrase>pictures</phrase>
			</indexes>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Another way to view data, including images, is to use the Picture operator. You create it by choosing <f family="Verdana" charset="0">
						<b>
							<inlineAttr line-through="false">
								<c val="#000">Picture</c>
							</inlineAttr>
						</b>
					</f> from the <f family="Verdana" charset="0">
						<b>
							<inlineAttr line-through="false">
								<c val="#000">Insert</c>
							</inlineAttr>
						</b>
					</f> menu. </p>
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						<ml:str xml:space="preserve">spectogram.txt</ml:str>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The picture operator displays 255 bit images to the screen, so data should be <b>
						<u>
							<link href="./scale.xmcd" title="Links to section" popup="false">scaled</link>
						</u>
					</b> to the 0 to 255 range.</p>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Try right-clicking on this picture operator to see more options.</p>
			</text>
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				<inputs>
					<ml:id xml:space="preserve" subscript="s" xmlns:ml="http://schemas.mathsoft.com/math30">M</ml:id>
				</inputs>
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					<ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">bits</ml:id>
				</outputs>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">When you click on a picture operator, you can zoom, select rows and columns of your data, or select areas, by choosing appropriate buttons from the <f family="Verdana" charset="0">
						<b>
							<inlineAttr line-through="false">
								<c val="#000">Picture toolbar</c>
							</inlineAttr>
						</b>
					</f>.</p>
			</text>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Right-click on the picture operator and select <b>Properties</b> to see a variety of useful properties for exporting selected data. We used this dialog to define the bits variable.</p>
			</text>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">You can use the picture operator to display color images as well, by providing the Red, Green, and Blue components as separate matrices. For example, here is a spectral map that gives the mappings for the red, green, and blue components given the levels 0 to 255 in a grayscale image like the one above:</p>
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							<ml:id xml:space="preserve">red</ml:id>
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				<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">We can also display this matrix as a contour plot. In this example, we've applied the Fire colormap from the Advanced tab. Double-click on the plot to see all settings used to create this plot.</p>
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			<picture>
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