Types of Errors: Study with Video Lessons, Practice Problems & Examples

In experimental science, understanding errors is crucial. Indeterminate errors, or random errors, arise from uncontrollable variables, leading to inconsistent measurements, such as varying weights. In contrast, systematic errors stem from flaws in equipment or design, producing consistent deviations, like a scale always reading 0.05 grams too heavy. Recognizing these errors enhances accuracy in measurements, emphasizing the inherent uncertainty in all experimental data, known as experimental error. This knowledge is vital for improving precision in scientific experiments and calculations.

Types of Error

As we discussed earlier, we said that any type of calculations done has some level of uncertainty involved with it. This we termed experimental error. Now here we're going to talk about the 2 exact terms for the different types of errors that are commonly occurring. We're going to say this first type of error is referred to as an indeterminate error. We're going to say it occurs from uncontrollable variables in an experiment.

It can occur at any time in a positive or negative magnitude, can never be corrected, and is not reproducible. So for example, you take a weight. You know that it should weigh 10 grams, but in some instances, you get 9.8 grams. Other instances you get 10.35 grams. There is no consistency to the values here. They'll be too high by a certain value or too low by another, so there are negative and positive magnitudes. We call this random error. Now, the next type of error, which is also called deterministic error, occurs from a problem with the machinery or a design flaw in the experiment. So it occurs always in the same magnitude, can be corrected, and is reproducible.

Let's say you have a weight that's 10 grams and you have a weight that's 12 grams. You weigh the weight that's 10 grams and you get a reading of 10.05 grams. You know that this standard weight is supposed to weigh 10 grams, but here it's giving us a magnitude that's 0.05 grams too heavy. So if this is a systematic error, which is the type of error we're dealing with here, then we should expect this 12 gram weight to come out 0.05 grams too heavy. It's consistently giving us the same value, the same magnitude.

It is always positive under certain circumstances or always negative under other circumstances. So there is consistency with systematic error. The beauty of this type of error is that if you can find it, you can correct it thereby minimizing the type of error that will pop up when you do a calculation. So remember, all types of measurements have a level of uncertainty associated with them called experimental error. More specifically, we can talk about random error versus systematic error.

Knowing this, attend to the example question that's left here below. Don't worry. Just come back and see how I answer that same exact question.

Types of Errors

So for example 1, it states that an uncalibrated pipette is used in the titration of 25 mL of 0.250 molar potassium permanganate with 50 mL of nitric acid. If the pipette delivers 23.120 plus or minus 0.02 mL, what can be said about the possible errors observed? Alright, typically, when they give us a pipette, it's supposed to be calibrated. On the first day in the lab, usually, you set up a calibration curve, and that lets you calibrate your pipette. Whenever we have an uncalibrated pipette, therefore, we confront a systematic error.

Remember, systematic error can be identified and corrected. To correct the uncalibrated pipette, as mentioned, you set up a calibration curve. Now, what else could be said about possible errors in terms of this statement? Let's assume that you've already calibrated it or it's still uncalibrated, and you're delivering your mL aliquots of nitric acid. Here, it's stated with a plus or minus 0.02 mL.

Suppose that in certain deliveries, you get plus 0.02 mL and in others, you get minus 0.02 mL from what you're supposed to deliver. If it varies, being positive sometimes and negative at others, this would be an example of random error. That's a second type of error we could possibly discuss in this scenario. The main focus, however, should be that you're dealing with an uncalibrated pipette, which introduces a systematic error. This is acceptable because this type of error can always be detected and corrected later.

Now, what effect will having an uncalibrated pipette have in terms of your calculations dealing with uncertainty? Later on, we will learn how to calculate absolute uncertainty, relative uncertainty, and percent relative uncertainty from our calculations. In those cases, we're addressing random error. In this scenario, where we predominate with systematic error, we approach these types of questions differently. If you're facing systematic error, how would we calculate our overall error?

Suppose we wanted to deliver 4 portions of this acid, and each portion was to be 23.120 plus or minus 0.02 mL. When dealing with systematic error and aiming to deliver it 4 times, you multiply both values by 4. This means that when we're delivering 92.480 mL, there would be an uncertainty of plus or minus 0.08 mL. This is specifically true when dealing with an uncalibrated pipette affected by systematic error. Later on, when learning about terms like absolute uncertainty, relative uncertainty, and percent relative uncertainty, we wouldn’t approach the problem in the same way.

In these cases, again dealing with random error demands a completely different approach. For now, just remember, an uncalibrated pipette leads to systematic error, which is fortunately detectable and correctible. Random error, however, is inconsistent. Sometimes, it'll show as a plus a certain amount; other times, it could be minus a certain amount. There’s no discernible connection between the different deliveries of your acid in this case. Random error can’t be detected consistently nor corrected directly.

For this situation, there are two possibilities: systematic error because the pipette is uncalibrated, and if it’s presenting a plus or minus volume variation, then that could be an example of random error. Now that we've analyzed this example, let’s move on to example 2 to determine from the statements provided if it's random error or systematic error.

Types of Errors

So here we have to state whether the errors are random or systematic for each of the following. So for the first one, it says the analytical measuring pipette in the lab consistently delivers 25.0 ± 0.03 milliliters. Now, the fact that it consistently delivers such a volume, we would say that the 25 ml's represents a systematic error, which would mean that we could go and detect this type of error and try to correct it. Now, here, the uncertainty involved is ±. So it has a positive and negative magnitude. Because it could either be +0.03 ml's too much or -0.03 ml's too little, we would say that this portion here is connected to random error.

So within a value, we can have both types of errors present. In option B, it says I weigh an analyte sample 4 times and obtain the following numbers. So, I get 1.110, 1.392, 1.040, and 1.850. We can see that the four numbers really have no consistency to them. They are kind of all over the place.

So we would say here that this is definitely an indicator of random error. Okay, so random error here would be harder to control. We wouldn't be able to reproduce the same results every time, so we wouldn't be able to correct the mistake that is occurring. Whereas the first one had a combination of both errors due to this uncertainty ± portion that's present, the second one because we're measuring and there's no uncertainty with these numbers, we would say that this is clearly random error.

Here’s what students ask on this topic:

What is the difference between random error and systematic error?

Random error, also known as indeterminate error, arises from uncontrollable variables in an experiment, leading to inconsistent measurements. For example, weighing the same object multiple times might yield different results each time. Systematic error, or determinant error, stems from flaws in equipment or experimental design, producing consistent deviations. For instance, a scale that always reads 0.05 grams too heavy will consistently give incorrect measurements. Understanding these errors is crucial for improving the accuracy and precision of scientific experiments.

How can systematic errors be identified and corrected in an experiment?

Systematic errors can be identified by comparing measurements with known standards or using different methods to measure the same quantity. If consistent deviations are observed, it indicates a systematic error. Once identified, these errors can often be corrected by calibrating the equipment, adjusting the experimental design, or applying correction factors to the data. Recognizing and correcting systematic errors is essential for ensuring the reliability and accuracy of experimental results.

Why is it important to understand the types of errors in experimental science?

Understanding the types of errors in experimental science is crucial because it helps improve the accuracy and precision of measurements. Random errors, caused by uncontrollable variables, and systematic errors, resulting from equipment flaws or design issues, both contribute to the uncertainty in experimental data. By identifying and addressing these errors, scientists can enhance the reliability of their results, make more accurate conclusions, and improve the overall quality of their research.

Can random errors be completely eliminated in an experiment?

Random errors cannot be completely eliminated because they arise from uncontrollable variables that affect measurements in unpredictable ways. However, their impact can be minimized by increasing the number of measurements and using statistical methods to analyze the data. Averaging multiple measurements can help reduce the effect of random errors, leading to more accurate and reliable results. Despite this, some level of uncertainty will always remain in experimental data.

What are some common sources of random error in experiments?

Common sources of random error in experiments include fluctuations in environmental conditions (such as temperature and humidity), variations in measurement techniques, and inherent limitations of the measuring instruments. Human factors, such as inconsistent handling of equipment, can also contribute to random errors. These errors lead to variations in measurements that are unpredictable and can be either positive or negative, affecting the overall accuracy of the experimental results.