Experimental Error: Videos & Practice Problems

Experimental error encompasses both accuracy and precision in scientific measurements. Accuracy refers to how close a measurement is to the true or accepted value, while precision is about the repeatability of measurements—how close they are to each other. Experimental errors can be random or systematic. Random errors result in measurements that fluctuate unpredictably, being sometimes too high or too low, and can be minimized by taking multiple measurements and averaging them. Systematic errors, on the other hand, produce consistently biased results that are either always too high or too low, and can often be corrected by adjusting the experimental setup. Percent error is a valuable metric for evaluating the precision of measurements, calculated using the formula:

$\left[\frac{(\mathrm{experimental\; value}-\mathrm{theoretical\; value})}{\mathrm{theoretical\; value}}\right]\times 100$

A percent error less than 10% is typically considered acceptable. Understanding and identifying these errors are crucial for improving the reliability of experimental results.

Experimental Error

In this video we take a look at experimental error. Now experimental error is connected to two 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 two 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 are your results 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 four 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 can you get to the actual agree upon value for an object when you 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 one gram too heavy, then all of a sudden it's 2g, 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 and 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 weigh an object and it's consistently 1g 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 2g too light, and it's always that no matter what object I measure, it's always 2g 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 2g 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 2g less than what they should be. You wouldn't know that. Now in most cases a percent error of less than 10%, it will be acceptable. OK, so if you're doing your experiment, you can test for your percent error and see is it within these guidelines? If so, it'll 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 that 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. The theoretical value is your known value. So let's 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 way it should be. So that is your theoretical value. You weigh it out a bunch of times and you get 24.8g. That is your experimental value. You plug those in and see what your percent error is. Since the numbers are pretty close to one another, it's 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, not only 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 one 2-3 and four, 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 in order to minimize any errors. Remember we talked about this up above. Random errors are unpredictable. On the same scale that you're measuring something. It may give you a total that's 1G too high. And then another instance it may give you a math that's 2G too light. It's always fluctuating between being too much or too 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 one is at least true.

The results of an experiment are consistently greater than expected or less than expected. So 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 be indicates A systematic error, so this would not be an option.

Refining the parameters of the experiments help to eliminate any errors. Now remember, a random error is unpredictable, so there's nothing really we can do on 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 because the design of the experiment may be flawed. So we go back and we tweak it a little bit to make it better. This helps to eliminate systematic errors.

Finally, the existence of the error is hard to determine. So 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, it'll 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 that if an error does occur or not. So this would be indicative of a systematic error.

So out of my four options, only option one represents a 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, we can't easily detect it.

The only way I would know if something is giving me a number that's too high or too low is that if I have the agreed upon value ahead of time, which is called your theoretical value. OK, without that value, you won't know for sure if a systematic error is occurring. 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. Here. We say 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 drive out all of the water, so this is definitely a systematic error. All you got 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.

The scale used has not been properly calibrated, so this is a big thing. Anytime you start a lab you they always tell you to calibrate your pipettes, calibrate your beer rats, calibrate on 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 got to do to get rid of that error is calibrate the scale.

Next, air flow near the balance causes the precise mass to vary All right, so air flow. It's hard to control the flowing of air as you're opening up the scale and putting your your object and then closing the door behind it. So air flow is something that's outside your realm of control. Because of this, it's a random error. That air flow won't always be present, so it won't always affect the mass that you have.

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 systematic error? Or 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 she wrote down the wrong number and didn't go back and check it is a flaw in 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 fourth option would fall under systematic error as well. So here we'd say that 1-2 and four 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 error and random error and how they together give us a good impression of what experimental error could be.

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 that can result in values being too high or too low. They are often caused by uncontrollable variables and can be minimized by taking multiple measurements and averaging them. Systematic errors, on the other hand, are consistent biases that cause measurements to be either always too high or too low. These errors are often due to flaws in the experimental setup and can be corrected by adjusting the procedure or equipment.

How can you minimize random errors in an experiment?

To minimize random errors, you should take multiple measurements and calculate the average. This approach helps to balance out the unpredictable fluctuations that characterize random errors. Additionally, ensuring consistent experimental conditions and using precise instruments can further reduce the impact of random errors.

What is percent error and how is it calculated?

Percent error is a measure of the accuracy of an experimental value compared to a theoretical value. It is calculated using the formula:

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

A percent error less than 10% is typically considered acceptable in most experiments.

What are some common sources of systematic errors in experiments?

Common sources of systematic errors include improperly calibrated instruments, flawed experimental design, and environmental factors such as temperature and humidity. For example, using a scale that has not been calibrated correctly can consistently give measurements that are too high or too low. Correcting these errors often involves adjusting the experimental setup or recalibrating the instruments.

Why is it important to distinguish between accuracy and precision in experimental measurements?

Distinguishing between accuracy and precision is crucial because they address different aspects of measurement quality. Accuracy refers to how close a measurement is to the true or accepted value, while precision indicates the repeatability of measurements—how close they are to each other. Understanding both concepts helps in identifying and correcting errors, thereby improving the reliability of experimental results.