Calculating Percent Error
In your everyday life, it's pretty common to make estimates of values rather than taking the time or brainpower to use exact ones. If someone asks you how far the nearest gas station is, you'll probably say something like, "It's about 5 miles away." That's an estimate.
Yes, making estimates is a common practice in our daily lives. However, it's important to understand that estimates may not always be accurate. This is where the concept of percent error comes into play. Percent error is a way to measure the difference between an estimated value and the actual value, expressed as a percentage.
To calculate percent error, you need two values: the estimated value (also called the experimental value) and the actual value. The formula for percent error is:
Percent Error = ((|Actual Value - Experimental Value|) / |Actual Value|) * 100
Let's say you estimated the distance to the nearest gas station to be 5 miles, but the actual distance is 6 miles. Using the formula, the calculation would be:
Percent Error = ((|6 - 5|) / |6|) * 100
Percent Error = (1 / 6) * 100
Percent Error = 16.67%
In this case, the percent error is 16.67%, indicating that your estimate was 16.67% off from the actual value.
It's important to note that percent error can be positive or negative. A positive percent error means that your estimate was higher than the actual value, while a negative percent error means that your estimate was lower than the actual value. The absolute value is taken to ensure that the percent error is always positive.
Percent error is a useful tool for evaluating the accuracy of estimates or experimental data. It allows you to quantify and compare the difference between the estimated and actual values, giving you a better understanding of the validity of your estimates.