To calculate the percentage error for measuring aluminum density, we can replace the indicated values of 2.45 g/cm3 with the experimental value and 2.70 g/cm3 with the assumed value. The accepted value is a number or value that scientists and the public consider to be true. The test error is “|99.3 degrees Celsius – 100.0 degrees Fahrenheit| “The smaller the difference between the average and the true value, the greater the accuracy.” If the experimental value is less than the accepted value, the error is negative. If the experimental value is greater than the accepted value, the error is positive. Often, an error is reported as the absolute value of the difference, in order to avoid confusion of a negative error. The percentage error is the absolute value of the error divided by the accepted value and multiplied by 100%. When we discuss the measurements or results of measurement instruments, these are different concepts that are often confused. In this section, four important ideas are described and the differences between them are noted. The first difference is between accuracy and accuracy. “The smaller the difference between the measured value of repeated measurements of the same amount, the greater the accuracy.” As mentioned above, the more measures there are, the closer we can get to the knowledge of the actual value of a quantity.
For several measurements (replications), we can evaluate the accuracy of the results, and then use simple statistics to estimate how close the average value would be to the actual value if there was no systematic error in the system. The average value deviates less from the “real value” as the number of measures increases. Precision refers to the compliance of the measurement and the actual value and does not tell you about the quality of the instrument. The instrument can be of high quality and still cannot have the true value. In the example above, it has been assumed that the purpose of the clock is to measure the position of the Sun as it appears to be moving over the sky. However, in our time zone system, the sun is only placed just above the head if you are in the middle of the time zone. If you are at the eastern end of the time zone, the sun is just above the head around 11:30 a.m., while on the western periphery, the sun is just above the head around 12:30 p.m. On both sides, the 12-hour reading does not correspond to the phenomena of the sun at the local zenith and we might complain that the clock is not accurate.