Experimental Error - Online Tutor, Practice Problems & Exam Prep

Experimental error is categorized into random and systematic errors. Random errors indicate a lack of precision, leading to unpredictable fluctuations in measurements, while systematic errors reflect a lack of accuracy, consistently skewing results in one direction. To minimize random errors, multiple measurements should be averaged. The percent error formula, given by $|\mathrm{experimental\; value}-\mathrm{theoretical\; value}|/\mathrm{theoretical\; value}100$, helps assess measurement precision. Understanding these errors is crucial for accurate scientific experimentation.

Experimental Error

In this video, we take a look at experimental error. Now experimental error is connected to 2 other concepts we've discussed before in the past, the ideas of accuracy and precision. Now, we're going to say when any calculation is done, there is a level of error involved. We're going to say error itself can be grouped into 2 major categories. We have our random errors and we have our systematic errors. We're going to say when it comes to random error, random error is basically the lack of precision. And remember precision is how close your results are to one another. So if you take 4 measurements and they're all close to one another, then you are precise. Systematic error is a lack of accuracy. Now you can have 4 measurements that are close to one another and therefore are precise, but they may not be accurate if they're far away from the actual value. So accuracy is how close you can get to the actual agreed-upon value for an object when it comes to measuring it. Now we're going to say here that random errors are unpredictable and can lead to results that are either too high or too low. Basically, as the student within the lab, you have basically no control over random errors. It could be the result of random occurrences that happen just in unperceived ways. So it's really hard to minimize these types of errors. Now when we say it could be either too high or too low that means that if I, let's say, measure out an object and it is 1 gram too heavy, then all of a sudden it's 2 grams too light. And it fluctuates back and forth between being either too heavy or too light in terms of its mass. This would be an example of random error. Now here's the thing. Because our results can either be too high or too low, the best way to approach random error is to take several measurements over time. If you take several measurements and then average out all those measurements that will help to reduce your random error. Systematic error is different. Systematic errors are more predictable and can lead to results that are always too high or always too low, but not both. So let's say I weigh an object and it's consistently 1 gram too heavy. That is a systematic error. The error is always too high. Or I use another scale and I measure out something and it's consistently 2 grams too light. And it's always that. No matter what object I measure, it's always 2 grams less. That's a systematic error. That's something that I can basically, adjust and expect to occur because I know it's going to be 2 grams too light each time. But here's the thing. Whereas random errors are easier to spot because you'll get measurements that are too high and too low randomly, systematic errors are harder to spot. You may not know that you have a systematic error because let's say you take that object and you measure it several times and it keeps giving you that same exact value. You think that you are accurate. But in reality, the scale is giving you numbers that are 2 grams less than what they should be. You wouldn't know that. Now in most cases, a percent error of less than 10% will be acceptable. So if you're doing your experiment, you can test for your percent error and see is it within these guidelines. If so, it will be an acceptable answer. Percent error itself is experimental value minus theoretical value in absolute brackets which means that even if you get a number that's negative inside of here, because it has absolute brackets it'll be a positive value. And then it's divided by your theoretical value and you multiply it times 100. Now remember this times 100 is what gives us our percentage value, similar to mass percent and other concepts that we've talked about in other chapters. We're going to say the percent error formula is a useful tool for determining the precision of your calculations. Huge differences in percent error, huge values in percent error means that your numbers are not very precise. Now we're going to say here that the experimental value is your calculated value. You do the experiment, you crunch some numbers, you do the math, you get this total. That's your experimental value. You say, "I'm weighing out an object." And in the literature, in your manual, it says that it should weigh 25 grams. In the literature, it tells you that's the weight it should be so that is your theoretical value. You weigh it out a bunch of times and you get 24.8 grams. That is your experimental value. You'd plug those in and see what your percent error is. Since the numbers are pretty close to one another, it's safe to assume that your percent error wouldn't be that high. So it looks like it would be somewhat of an acceptable value. Now now that we've seen the different classifications of error, let's see if you guys can tackle these example questions. Attempt to do the first one on your own, but if you get stuck, don't worry. Just come back and take a look at my explanation on the best answer here. Here, I've done it as 1, 2, 3, and 4, meaning that more than one answer could be the correct choice. So pay attention to what we talked about up above to answer this question on random errors.

Random Errors

Which of the following features are indicative of random errors? So the first option, doing numerous measurements and taking the average to minimize any errors. Remember we talked about this up above. Random errors are unpredictable. On the same scale that you're measuring something, you may get a total that's 1 gram too high, and then another instance it may give you a measurement that's 2 grams too light. It's always fluctuating between being too much or too low. Here, a way to minimize random error is to take numerous measurements and then take the overall average of those measurements. So yes, this is indicative of a random error. So we know that option 1 is at least true.

The results of an experiment are consistently greater than expected or less than expected. Here it's saying consistently. Consistently would imply that it's a predictable outcome. So this would indicate that we have a systematic error. Remember, systematic errors will consistently give us a value that's greater than expected or less than expected. Never both. So, this would not be an option.

Refining the parameters of the experiments helps eliminate any errors. Now remember, a random error is unpredictable. So there's nothing really we can do ourselves to stop it from happening. All we can do is help to minimize random error by taking several measurements. Here, if we're going to redefine or refine the parameters, that means that we're dealing with a systematic error. One reason that systematic errors occur is that the design of the experiment may be flawed. So we go back and we tweak it a bit to make it better. This helps to eliminate systematic errors.

Finally, the existence of the error is hard to determine. Here it's easy to see that we have a random error. You measure something several times, and you get numbers that are too high and too low. It's always fluctuating back and forth between being too high or too low. We know that's not normal, so we know there's a problem there. A systematic error, though, will consistently give us a number that's too high or give us a number that's too low. Because it's consistently doing this, it's hard for us to determine if an error does occur or not. So this would be indicative of a systematic error. So, out of my four options, only option 1 represents random error.

Now that we've done this example, try to do the final one. See if you get the same answer that I get when you come back and take a look at my explanation.

Systematic Error

Which of the following represent a systematic error when measuring the mass of an anhydrous object? Anhydrous means that the object has been completely dried out. All the water has been left out of the object or evaporated out of the object. Now when it comes to a systematic error, it's predictable in the sense that it's always going to give us a value that's too high or too low from the agreed upon value. But in its predictability, there is some problem involved. Because of this predictability, if I have the agreed upon value ahead of time, which is called your theoretical value, I cannot know for sure if a systematic error is occurring without that value. A good thing about systematic error is if you know that you have it, all you have to do is correct the design of your experiment. By correcting it, you can eliminate that error. Knowing this now, let's take a look at the options:

1. You weigh the object before all the water has evaporated. So you're weighing an object, it's supposed to be completely dry, but you haven't given enough time to dry out. So you're going to get a mass that's too high. This is a flaw within the experiment. You didn't wait long enough for you to dry out all of the water. So this is definitely a systematic error. All you have to do to correct it is wait more time. Always wait as long as possible in terms of drying. Get all the water out, and then you'll get the right mass of the dry object.
2. The scale used has not been properly calibrated. So this is a big thing. Anytime you start a lab, they always tell you to calibrate your pipettes, calibrate your burettes, calibrate your scales. This ensures that the number that you're going to get is as close to the agreed upon value as possible. So again, that's another flaw within the system. All you have to do to get rid of that error is calibrate the scale.
3. Airflow near the balance causes the precise mass to vary. Airflow is hard to control as you're opening up the scale and putting your object inside and then closing the door behind it. So airflow is something that's outside your realm of control. Because of this, it's a random error. That airflow won't always be present so it won't always affect the mass that you have.
4. You write down the incorrect mass of the anhydrous object. So here, you didn't write down the correct number. This is a little bit tricky. Could this be a systematic error? Could this just be a random error on your part? Because you're not always going to write down the wrong number, we're going to say here that this could fall under a systematic error because within the design of your experiment, you're supposed to always double-check, triple-check all your numbers and values to make sure they make sense. The fact that you wrote down the wrong number and didn't go back and check it is a flaw in the design of your experiment. You tell yourself, if I write down a number, I have to look at it multiple times to make sure it's the correct number that I'm writing. So we could say that the 4th option would fall under systematic error as well. So here we'd say that 1, 2, and 4 are your systematic errors, although 4, you could be open to saying that it's a random error as well because you're not always going to make that mistake. So, guys, remember the difference between systematic

Here’s what students ask on this topic:

What is the difference between random error and systematic error in experimental measurements?

Random errors are unpredictable fluctuations in measurements, often due to uncontrollable variables, leading to a lack of precision. They can cause results to be either too high or too low. To minimize random errors, multiple measurements should be taken and averaged. Systematic errors, on the other hand, are consistent deviations from the true value, caused by flaws in the experimental setup or equipment, leading to a lack of accuracy. These errors consistently skew results in one direction, either too high or too low. Identifying and correcting the source of systematic errors, such as recalibrating equipment, can help eliminate them.

How can you minimize random errors in an experiment?

To minimize random errors, take multiple measurements and calculate the average. This approach helps to balance out the unpredictable fluctuations that characterize random errors. Additionally, ensuring a controlled environment and using precise instruments can further reduce the impact of random errors. However, since random errors are inherently unpredictable, completely eliminating them is challenging. Averaging multiple measurements remains the most effective strategy for minimizing their effect on experimental results.

What is the formula for calculating percent error, and how is it used?

The formula for calculating percent error is:

$\left|\frac{\mathrm{experimental\; value}-\mathrm{theoretical\; value}}{\mathrm{theoretical\; value}}\right|100$

This formula helps assess the precision of your measurements by comparing the experimental value to the theoretical value. The absolute difference between these values is divided by the theoretical value and then multiplied by 100 to express the error as a percentage. A lower percent error indicates higher precision, while a higher percent error suggests less precise measurements.

What are some common sources of systematic error in experiments?

Common sources of systematic error include improperly calibrated equipment, flawed experimental design, and consistent environmental factors. For example, a scale that is not calibrated correctly will consistently give incorrect measurements. Similarly, if an experiment is designed in a way that introduces bias, such as not allowing enough time for a substance to dry completely, it will lead to systematic errors. Identifying and correcting these sources, such as recalibrating equipment and refining experimental procedures, can help eliminate systematic errors.

Why is it important to distinguish between random and systematic errors in scientific experiments?

Distinguishing between random and systematic errors is crucial for accurate scientific experimentation. Random errors affect the precision of measurements and can be minimized by averaging multiple measurements. Systematic errors, however, affect the accuracy and consistently skew results in one direction. Identifying the type of error helps in applying the correct method to minimize or eliminate it, ensuring the reliability and validity of experimental results. Understanding these errors also aids in interpreting data correctly and improving experimental design.