Introduction
One of the main attributes of laboratory work and the performance of domestic tasks is the accuracy of measurements. The accuracy of measurements should be defined as the reliability of obtaining them compared to some valid value of that quantity. Standards with absolute accuracy that can be used for calibrating measurements are often used as the actual value.
For example, a reference centimeter may be measured on a carefully designed ruler, the length measurement of which will give the most accurate result. At the same time, it is fair to admit that highly accurate measuring instruments are not always available, so improvised instruments can be used for these tasks with a certain degree of accuracy. In the present laboratory work, a quantitative comparative analysis of the accuracy of π values measurement with diameter and circumference using an uncalibrated improvised ruler made manually and a proper ruler, the reliability of which is maximum. The purpose of the work is to determine the value of the percentage error that is made by measuring the handmade ruler compared to the reference value of the actual instrument.
Data and Analysis
Table 1 shows the results of direct measurements of the π value for the individual observation and the collective data from the class. As can be seen from the percent error bar, the difference between the actual π value (3.141592…) was approximately 5.75%, indicating a high level of accuracy and, consequently, a low level of error and bias. In other words, the measurements made with a handmade ruler were generally highly accurate.
Table 1. Measurement results for a handmade ruler
Table 2 shows the results of direct measurements and indirect calculations for an accurate, pre-calibrated ruler that provides reliable data. As one can see from this table, the percentage error with such a ruler dropped to 0.91%, indicating much higher accuracy and a very low probability of making an error. In other words, the measurement error dropped precipitously when using a proper ruler.
Table 2. Measurement results for the proper ruler
Figure 1 shows the results of the normalized distributions for each of the two ruler types plotted on the scatter plots. The orange data corresponds to the proper ruler, while the blue data is characteristic of the handmade ruler. As can be seen from the figure, for a given value with a higher percentage error, the bell-shaped distribution is wider and flattened, in contrast to the more accurate data for the calibrated ruler.
This distribution may indicate that the data for the handmade ruler is more scattered around the mean and thus has a higher standard deviation value (Bloomenthal, 2022). In other words, each distribution measurement deviates more strongly from the mean value than if a proper ruler were used. The peaks of both plots are in the region of their mean values, which are 3.196 for the handmade ruler and 3.172 for the proper ruler.
Conclusion
The present laboratory work was designed to investigate the accuracy of the π value calculations using two rulers, one handmade and the other calibrated, and shows accurate values. The results demonstrated that using the handmade ruler increased the percentage error by about five percentage points, to 5.75%, compared to 0.91% for the proper ruler. Meanwhile, both percentage error values were relatively low, so the results were highly accurate. The normalized distributions for the handmade ruler were broader and flattened, corresponding to a greater scatter in the data than the proper ruler. In other words, the overall conclusion was that the proper ruler showed more reliable and ordered data than the handmade one.
Reference
Bloomenthal, A. (2022). Bell curve definition: Normal distribution meaning example in finance. Investopedia. Web.