![]() ![]() The best adjustment will bring about one-half of the data points beneath the ruler, evenly distributed along the line. Straight Line Fitting Place a transparent ruler or drafting triangle on your graph and adjust its position so that the edge is as close as possible to all the data points. t 2 is plotted, a straight line should be obtained with slope = g/2 and y-intercept = 0. It is difficult to tell whether the data plotted in the first graph above agrees with this prediction. In the example given above, it is expected that the falling object's distance varies with time In these situations, you will be asked to fit a straight line to the data points and to determine the slope and y-intercept from the graph. Straight-line Graphs In many of the exercises in this manual, you will be asked to graph your experimental results in such a way that there is a linear relationship between graphed quantities. This curve now indicates the average trend of the data, and any predicted values should be read from this curve rather than reverting back to the original data points. Do not connect the data points by straight-line segments in a dot-to-dot fashion. A French curve is useful for drawing curved line segments. The curve will not necessarily pass through all the points, but should pass as close as possible to each point, with about half the points on each side of the curve this curve is intended to guide the eye along the data points and to indicate the trend of the data. Curves Draw a simple smooth curve through the data points. A drafting template is useful for this purpose. ![]() If more than one set of data is to be shown on a single graph, use other symbols (e.g. Data Points Enter data points on a graph by placing a small dot at the coordinates of the point and then drawing a small circle around the point. Note in this connection that it is not always necessary to include the origin ('zero') on a graph axis in many cases, only the portion of the scale that covers the data need be plotted. In the illustration, scales have been chosen to give the graph a roughly square boundary you should avoid choices of scale that make the axes very different in length. ![]() Frequently the scale must be considerably coarser than this limit, in order to fit the entire plot onto a single sheet of graph paper. A scale finer than 1 div/mm would provide no additional plotting accuracy, since the data from the meter stick are only accurate to about 0.5 mm. For example, data from a meter stick (which has 1 mm graduations) should be plotted on a scale no finer than 1 division = 1 mm. Scales should be made no finer than the smallest increment on the measuring instrument from which data were obtained. Other choices (e.g., 0.3) make plotting and reading data very difficult. On coordinate paper, every 5 th and/or 10 th line is slightly heavier than other lines such a major division-line should always represent a decimal multiple of 1, 2, or 5 (e.g., 0, l, 2, 0.05, 20, 500, etc.). ![]() Choice of Scale Scales should be chosen in such a way that data are easy to plot and easy to read. Axis Labels Each coordinate axis of a graph should be labeled with the word or symbol for the variable plotted along that axis and the units (in parentheses) in which the variable is plotted. Also, write your name and the date on the plot as well for convenient reference. Title Every graph should have a title that clearly states which variables appear on the plot. Use a sharp pencil (not a pen) to draw graphs, so that the inevitable mistakes may be corrected easily. Figure 1 Graph Paper Graphs that are intended to provide numerical information should always be drawn on squared or cross-section graph paper, 1 cm × 1 cm, with 10 subdivisions per cm. ![]()
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