Everything You Need To Know About Learn Experimental Data And Graph…

Let’s see how experimental data can be graphically depicted. We do this to find the relationship between physical constraints that we collected data from the experiments. We can see the relationship graphically. Also, their relationship is very easy to understand using a graph. Let’s we see how to plot a graph by using data from an experiment.

Graphical representation of experimental data

It is often difficult to grasp the relationship existing between the numbers by examining
the values that we have tabulated. The graphical method is mostly used to discover such relationship. It gives a pictorial view of the results and makes it possible to interpret the data at a glance well.

Independent and dependent variables

In many experiments, we always change only one variable at a time. Next, observe the
corresponding values of another physical quantity, which suspect of relating to the first physical quantity.

The independent variable is the first of these quantities which always change by us. It is plotted on the abscissa scale (X-axis).  The dependent variable is the physical quantity which relates to the first. It is plotted on the ordinate scale (Y-axis).

Choice of scale

If we choose the range of scale correctly the graph will fit the entire graph sheet. Note the
range of values of the independent variable (X quantity) and the number of spaces
along the X-axis. Let we assume the range of X quantity as \b{d_x} and the number of spaces X-axis as \b{n_x} .  Choose a good scale for the main divisions on the graph paper that are
easily subdivided such as 1, 2, 5 and 10 are the best, 4 is sometimes used. But never use 3, 7, or 9 because of they difficult to read values from the graph. one\,division\,on\,the\,x-axis\,= \,\frac {d_x}{n_x} The same procedure should be used for the ordinate scale or Y-axis. but the divisions on X-axis scale and Y-axis scale need not be alike.The intersection of the two axes represent the zero values for both variables is not necessary. If the values to be plotted are exceptionally large or small, you can use some multiplying factor.

Labeling the axes

After deciding X-axis and Y-axis, write down the quantity with the proper unit. Then write the numbers along main divisions on the axes. The title should be written on the top of the paper.

Plotting and drawing the graph

Make small dots to locate the points and carefully encircle each point using a sharp pencil. The graphs are not always possible to make all points lie on a smooth curve or straight line. In such cases, a smooth curve should be drawn through the selected points. At least  5 points should be used to draw a reasonable straight line.  After selecting 5 points you want to find out the center of these 5 points by getting there averages. Let’s we assume these points are (x1,y1), (x2,y2), (x3,y3), (x4,y4) and (x5,y5). And the center of these five points is (\overline{x},\overline{y}) .

Center\,of\,the\,5\,points\,(\overline{x},\overline{y})= \,[\frac {x_1+x_2+x_3+x_4+x_5}{5},\,\frac {y_1+y_2+y_3+y_4+y_5}{5}]

After making the point of center on the graph Next. you can draw the line. At least six or five data points should be used to draw a reasonable straight line. The best straight line can easily be plotted by holding a ruler so that the data points are equally distributed either side of the line and the line should be on the center of points.

The shape of a graph

The shape tells us whether the dependent variable increases or decreases with the increase of the independent variable. If the points lie along a straight line, there is a linear relationship between the variables x, y. If the two variables x,y  are directly proportional to each other, they approach zero simultaneously. The line passes through the zero. Curves which are not pass through the zero (0,0) do not have direct proportion. But the lines are straight.

The slope or the gradient

We can find the slope of the line by dividing ∆Y by ∆X. To do that first we want to select two points P(xa, ya)  and P(xb, yb)  which lie far apart as possible as on the line. Do not select data point for P or Q.

The\,gradient\,of\,the\,line\,= \,\frac {y_b-y_a}{x_b-x_a}

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