The concept of experimental value is important in scientific experiments. Experimental value consists of the measurements taken during an experimental run. When taking experiment measurements, the goal is to arrive at a value that is accurate and precise. Accuracy relates to how close a single measurement is to the true theoretical value, while precision relates to how close the values of the measurements are to one another. For this reason, there are, at a minimum, three ways of calculating experimental value.
A Simple Experiment’s Experimental Value Is the Measurement Taken
Sometimes experiments are designed to be simple and quick, and only one measurement is taken. That one measurement is the experimental value.
Complex Experiments Require an Average
Most experiments are designed to be more advanced than the simple experiment type. These experiments often involve conducting several trial runs, which means more than one experimental value is recorded. During these types of experiments, taking the average of the recorded results is understood to be the experimental value.
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The formula for the experimental value of a set of five numbers adds all five together and then divides the total by the number 5. For example, to calculate the experimental value for an experiment with results of 7.2, 7.2, 7.3, 7.5, 7.7, 7.8 and 7.9, add them all together first to arrive at a total value of 52.6 and then divide by the total number of trials – 7 in this case. Thus, 52.6 ÷ 7 = 7.5142857 rounded to the nearest 10th gives the experimental value of 7.5.
Calculating Experimental Value Using the Percentage Error Formula
The percentage error formula, which is one of the calculations involved in error analysis, is defined as the comparison between the experimental value compared to the theoretical value. The accuracy of the result reveals how closely the experimental value is to the theoretical value.
The theoretical value is obtained from a scientific table and refers to the universally accepted value of a measurement, as in body temperature being 98.6 degrees Fahrenheit. The error analysis percentage error formula reveals how the experiment results deviate from expectations. Consequently, it helps determine the most significant errors and what effect those errors have on the final result.
The percentage error formula was devised to determine the precision of calculations, and it takes the form of:
Percent Error = (|[Experimental Value – Theoretical Value]| ÷ Theoretical Value) x 100
Rearranging this formula gives the experimental value. The closer the percent error is to 0, the more accurate are the experimental results. A number farther away from 0 indicates there are several instances of error – whether human error or equipment error – which could make the results inaccurate and imprecise.
For example, in an experiment that measures body temperature with a percent error of 1, the formula looks like 1 = (|[Experimental Value – 98.6]| ÷ 98.6) x 100. It becomes 1/100 = 0.01 = |[Experimental Value – 98.6]| ÷ 98.6. Calculating further, the formula gives 0.986 = |Experimental Value – 98.6|. In other words, the experimental value in simplified terms becomes 98.6 +/- 0.986, because the experimental value = theoretical value +/- error.
That the experimental value is in a range from 97.614 to 99.586 illustrates how much error there is in the conduct of the experiment, as already hinted at how far the percent error had been from the value of 0. Had the percent error been 0, the results would have been perfect, and the experimental value would have matched the theoretical value at exactly 98.6.