Types of Errors - Video Tutorials & Practice Problems

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All calculations are associated with some level of uncertainty which we define as its error.

Types of Errors

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Types of Error

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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 gonna talk about the two exact terms for the different types of errors that are commonly occurring, we're gonna say this first type of error is referred to as an indeterminant error. We're gonna 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 wait 1010 g. But in some instances you get 9.8 g. Other instances you get 10.35 g, uh then you get 9.15 g. There is no consistency to the values here. They'll be too high by a certain value. Too low by certain value. So there is negative and positive magnitudes we call this random error. Now, the next type of error, which is also called determinant error Yeah, occurs from a problem with the machinery or a design flaw in the experiment. So occurs always in the same magnitude, can be corrected and is reproducible. So let's say you have a weight that's 10 g and you have a weight that's 12 g. You weigh the weight that's 10 g. And you get a reading of 10.5 g. You know that the standard weight is supposed to wait 10 g. But here it's giving us a magnitude that's 100.5 g 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 g weight to come out .05g too heavy. It's consistently giving us the same value, the same magnitude. It's always positive under certain certain certain circumstances or always negative and under other circumstances. So there's 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 attempt to do the example question that's left here below. Don't worry. Just come back and see how I answer that same exact question. Okay.

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So, for example, when it says an un calibrated pipette is used in the titillation of 25 mls of 250.250 molar potassium permanganate with 50 ml of nitric acid. If the pipette delivers 23.120 plus or minus 0.2 mls, what can be said about the possible errors observed? Alright, so typically when they give us a call a pipette, it's supposed to be calibrated on the first day in lab, usually set up a calibration curve and that lets you calibrate your pipette whenever we have an uncalculated pipette, therefore we have systematic error. Remember systematic error can be identified and corrected and to correct um calibrated pipette, like I said, you set up a calibration curve. Now, what else can we say about possible errors in terms of this statement? Well let's say that you've already calibrated it or it's still in calibrated and you're delivering your ml ml of nitric acid here? It's saying plus or minus 0.2 mls, let's say that in certain deliverance is you get um plus 0.2 mls and in other ones you get negative 0.2 ml of what you're supposed to get. If it varies where it's positive sometimes and negative sometimes then this would be an example of random error. Okay, so that's a second type of error we could possibly talk about in terms of this statement, but the main focus should be that you're dealing with an un calibrated pipette, therefore it's a systematic error, which is okay because you can always find out that error and correct it later. Now, what effect will having an uncalculated pipette have in terms of your calculations dealing with uncertainty? Well, later on we'll learn about how to calculate absolute uncertainty, relative uncertainty and percent relative uncertainty from our calculations in those cases. That's when we're dealing with random error in this case. Because we're dealing with predominantly systematic error, we would approach these types of questions differently. If you're dealing with systematic error, how would we calculate what our overall error is? Now let's say that we wanted to do four portions of this acid and each portion was this amount 23.120 plus or minus 0.2 mls. When you're dealing with systematic error and we want to deliver it four times, you would multiply both values by four. So that means that when we're delivering 92.480, it'd be uncertainty of plus or minus 0.8 mls. This is only true when we're dealing with an uncalculated Pipat. When we're dealing with systematic error later on, When we learned about the terms like I said before, absolute uncertainty, relative uncertainty and percent relative uncertainty, we would approach the problem the same way in those cases. Again, we're dealing with random error which requires us to take a totally different approach for now guys just remember um calibrated pipette is not something that you want to deal with because it creates systematic error? The beauty of it though is that systematic error can be detected and corrected later on. Random error. It's all over the place. There's no discernible pattern. Sometimes it'll give us plus a certain amount. Other times they'll give us minus certain amount. There's no way to see any any connection between the different deliverance is of your of your asset. In this case, random error can't be detected, it can't be corrected. So again guys for this one, we say that there's two possibilities systematic error because it's an calibrated and if it's giving us plus or minus amount of volume, then that could be an example of random error. Now that we've seen this example, move on to example two and see from the statements provided. Can you determine if it's random error or systematic error?

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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 plus or minus 0.3 mL. Now, the fact that it says it consistently is giving such a volume, we'd say that the 25 mls represents a systematic error, which would mean that we could go and detect this type of error um and try to find it and correct it. Now. Here, the uncertainty involved is plus or minus. So it has a positive and negative magnitude because it could either be plus 0.3 mls too much or minus 0.3 mls too little. We'd say that this portion here is connected to random error. So within a value we can have both types of errors present an option B. It says I weigh and analyze sample four times and obtain the following numbers. So I get 1.110, and 1.850. We can see that the four numbers really have no consistency to them. They're kind of all over the place. So we'd 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 won't be able to correct the mistake that's occurring. So whereas the first one had a combination of both errors because of this uncertainty plus or minus portion that's present the second one because we're measuring and that's there's no uncertainty with these numbers. We'd say that this is clearly random error. All right.