Understanding Accuracy and Precision in Physics

So good day to all of you. This is General Physics 1, a subject in STEM strands in Senior High School. And for our lesson 2, we'll talk about accuracy and precision. So these are our target competencies. So differentiate accuracy from precision. Differentiate random errors from systematic errors. And estimate errors from multiple measurements of physical quantities. So let's have this concept that a good result of measurement is achieved if error made is less or limited. Whenever you are measuring something, you're happy if your measurement is correct. So you can say that that is a good measurement because you expect it to be right and the error perhaps... Wala or kakaunti. And in measurement, gaya ng na-discuss natin in the previous lesson, measurement ay minsan hindi laging tama. Ang measurement merong nagkakaroon ng inaccuracy, nagkakaroon ng pagkakamali sa pagme-measure. That's why this concept of accuracy and precision are considered as prime factors so that we can understand this measurement better. Is it normal for errors to happen? Yes. Errors in measurement are unavoidable. It happens. And it is due to several factors and it cannot be random or systematic. And it can be random or systematic depending on how measurement is made. Errors cannot be avoided. Even the greatest minds in scientific community have made... Many, many, many errors. But in their errors, they have found the greatest invention that we enjoy in our present time. Okay, who is already familiar with darting? Or at least familiar with darting? So imagine you are playing dart and given five darts to hit the target. You are given four chances to play. The result of each play is illustrated below. Let's say for example, may naglalaro ng dart. At yung naglalaro ng dart, ay ganito yung naging result nya. So for number one, so yung limang darts, ayan, dyan sya napunta. So yung target nya ay nasa gitna at scattered yung dart. Sa number two naman, ayan. Malapit sa target. Sa number three, anlayo sa target, pero nakakonsentrate sa isang side. Tapos yung number four, medyo nakakonsentrate, tapos anlapit pa sa target. So ano yung interpretation natin dyan kung ilalagay natin siya sa context ng accuracy and precision. Yung number one, Accuracy is poor because darts are far from each other Precision is also far because darts are far from each other Number 2 Accuracy is good because it's close to the target Right? But why is its precision poor? Because the concentration of darts is not that much Unlike number 3 its precision is high because as you can see, the darts are almost side by side but it's far from the target, that's why its accuracy is low and number 4, its accuracy is high because it's near the target and its precision is high because all of its trials almost hit the same point of the dartboard so in that context, accuracy and precision are shown Here it is. Have you tried cooking or are you cooking but failed with the taste? Like what my father said, if it's too salty, add more sugar. If you add more, the sweetness will increase. So did you use the right measurement of the ingredients? So if you didn't reach the desired taste, the delicious taste of what you're cooking, what could be the factors for that? for the errors or errors that uh the meeting you so there There are some factors why errors occur in every measurement. First, the kind of measuring device used. So, the measuring device used is wrong. So, if the measuring device used is wrong, you expect that the result is erroneous. Methods in getting the measurement. It's very important that the one who measures is knowledgeable. in one, in using the measuring device and in the process per se of measurement. Because a little mistake from the one measuring the desired measurement, it will lead to an erroneous measurement. And number three is the condition under which the measurement is made. It can be the environmental factors can affect the temperature and other factors around. So the condition has also something to deal with having an error in measurement. And there are two types of errors. One is random error or unsystematic error. These are the errors that you don't expect and can happen instantaneously. randomly and it has no pattern. So inconsistent ito. Example, in your first reading, you thought it might be too small then the next reading might be too large so nobody can predict random error and this cannot be avoided even scientists doing their experiments. So nung una tingin mo ang basa mo ay mababa lang and then the next reading, ang laki naman ang pagbasa mo. So What can be a factor there? It can be the mirror used when it's wet or the lighting around it. And it is an example of a random type of error. The second one is systematic. Systematic error is consistent and repeatable error due to the kind of measuring devices as mentioned above. It is also due to flawed experimental design. As mentioned above, If you keep on having the same error, like every time you do this procedure, you're meeting the same result or error, it means there's nothing wrong with... there's nothing wrong with... I mean, you're the one measuring, there's nothing wrong with you. The only thing wrong is the design. or the process of measuring. So what you have to do is you have to modify or change the way you measure the the thing that you are measuring to prevent this kind of error, the systematic error. So to minimize errors in measurement, more trials must be made. In our time, in the time of COVID-19 pandemic, Before the vaccine was made, it was being tested not just once, not just twice, but thrice or even more times before it was released to the market and given a permit to be used by people. Why? Because in one, let's say for example, you tried it on one person and then you saw that Maganda yung result sa isang naturukan. Hindi mo pwedeng sabihin na, o pwede na tong gamitin ng general public. Kasi compared to the general public, that one is negligible. And it can lead to results na hindi good. Kasi sa isa mo lang siya tinry. That's why it is being tested into... thousands of volunteers so that you can see more viable results so that your measurement and your result is more solid and you are more precise more accurate and you are more far from having errors because what is best is the life of the person although we are not leaving statistics we are still doing research naapektohan o na negative side ng mga vaccines na ito. So somehow they represent the little percentage. that when the vaccine is tested, they are the little percentage that did not have a good result or what do you call that? Pag-respond to the vaccine. So the mean or average value of these trials will be taken to represent the entire set of data. From this, the degree of accuracy and precision can be determined. So, in the context of vaccine, which is the most effective? Which is the most accurate? Which is the lowest accuracy or the least effective? Now, let's talk about accuracy. So, accuracy, how close are you to the target? So, if we go back to the dartboard earlier, how close is it to the target of the dartboard? So, it is the closeness or nearness. of the measurement of the accepted value. Accuracy is expressed in terms of absolute error or percentage of error. Like this. So you have the formula AE equals absolute value of O or observed value or measured value minus the accepted value. So the accepted value is the standard value and the observed value or values are the value that was found when measuring or measured when measuring. So after finding the absolute error, you compute for the percentage error and to do that you divide Absolute error to the accepted value times 100. And for getting the percentage of accuracy, you subtract 100% to the percentage of error. So, for you to understand these formulas and the samples, let's have this example. So, an experiment. dropped a stone from a five-story building and hit the ground, taking the time to fall of three seconds. Based from the data collected, the experimenter was able to measure the acceleration of the stone to be 9.8 meters per second square. The actual value of the acceleration due to gravity is 9.8 meters per second square. What is the percentage of accuracy of the experiment? So, 9.8 is... Uh... fixed value of acceleration due to gravity. But when an experiment was done on a child, he computed, so this is an observed value, he computed 9.8 meters per second. So how far or close is this to the actual value of 9.8? So to know that, you compute for the percentage of accuracy. So first, you write the given. You have the accepted value or A. which is 9.8 meters per second and the observed value which is O is 9.7 meters per second square. So AE equals absolute value of 0 or O minus A. Substituting the value, you have 9.7 meters per second square minus 9.8 meters per second square. If you can see, it will result to a negative number. But since we have these parallel lines, this is called absolute value, we disregard or we get the absolute value disregarding the signs of the result, resultant value, negative 0.1. So, because it has an absolute value, it's 0.1 meters per second square. So to compute for the percentage error, you substitute the value of AE, which is 0.1 meters per second, and the value of AE, which is 9.8 meters per second squared. Dividing them gives you 1.02% times 100. Yeah. So the result, the percentage error I mean is 1.02%. So you will then subtract that. to the 100% to get the percentage of accuracy which is 98.98%. So, that's how close it is. or that's how accurate the actual value of gravity is. So, we can pause and go back to how we computed the AE, the percentage of error, and percentage of accuracy. Now let's talk about precision. Precision is the agreement of several measurements made in the same way. In illustration number 3 of the dart game, the darts flocked in almost the same area. Though far from the bullseye, we can say that the measurements made are precise. So it's far from the target, it's definitely not accurate, but its precision is... almost really precise. Precision is expressed in terms of deviation or percentage of deviation. It is expressed in terms of deviation and the formula below will help you determine the precision of one's measurement. So AD, this is AD not AE. So AD or absolute deviation equals Absolute value of the observed value or measured value minus the mean of several measurements. I said earlier, one of the good things about measurement is that for you to be able to get a precise data, you need to have many trials because the many trials will give you consistency. You can see in these trials how consistent are the values that you are getting. So, if the values that you can see are closer, you can say that the result or the measurement is consistent. So, after having found the AD or the absolute deviation, you get the percentage of deviation. And that is solved by dividing the AD to the... mean of several measurement times 100, and the percentage of precision is obtained by subtracting 100 from the percentage of deviation. So, for you to understand these formulas better, let's have this example. A student is doing a laboratory experiment about falling body. He obtained three trials in measuring the time of fall. of a ball three meters above the ground the measurements are summarized below so trial one 0.8 seconds trial two 0.79 seconds trial three 0.77 seconds the question now how precise or what is the percentage of precision of the students so the first thing that you need to do the given because is to determine the average of the three trials. Why are you getting the average of the three trials? Because you are trying to get the letter M. Min is also average. Okay? So with that, so you add the three values of each trial, which is 0.80, 0.79, and 0.77, adding up this three and dividing it to three. you get 0.787 seconds. So that is your mean. Now that you have your mean, you try to solve for the absolute deviation. And AD is... What do you call that? AD is O minus M or absolute value of O minus M. If you can see here, it's just one. But because of three trials, you will do it repeatedly. So, you will have three OM. You will have three subtractions of the observed value to the mean value. So, how is that? So, you have first trial, 0.80 minus the M. which is 0.787 quantity plus quantity of 0.787 79 seconds minus m which is 0.787 s quantity plus 0.77 for the third trial minus the m which is 0.787 divide them or perform i mean the operations so you subtract subtract subtract and after subtraction you add the measurements and divide them all by three so you get 0.011s so what do you do with that number so you now get the ad or the absolute deviation so what to do next is to find for the percentage of deviation and that is ad Divided by m times 100. So you just substitute the value. So the value of AD, which is 0.011, and the value of m, which is 0.787 seconds, times 100, that is 1.4%. And afterwards, you get the percentage of precision, 100 minus 1.4, and you have 98. So the 98.6 is that how precise yung mga measurement na nakuha doon sa activity nung bata doon sa example natin. So pwedeng balikan yung previous slide or yung sa part ng video para mas mapag-aralan yung tungkol sa precision. So just to reiterate, accuracy refers to how close a measurement is to a true accepted or target value. How close is it to the actual value, the most targeted, the most fixed value. Precision, when you are having reproductions or many trials, how consistent are the values you see. how close they are to each other. So that's precision. So for my students, please do these activities. So letter A, you have the situation that Johnny and Sally perform an experiment to measure the density of aluminum. So the actual value of the density of aluminum is 2.7 grams per milliliters. So when... John measured 2.649 grams per milliliter while Sally's measurement is 2.731 grams per milliliter. So John is lower and Sally is higher. And one look, but who among them has a closer value to the actual value of 2.7? So compute for the percentage of accuracy of both measurements. Please show your complete solution. And the next problem, in an outdoor activity or experiment, Tokyo is testing his football robot kicking a ball and hitting the goal. She obtained four trials or four values measuring the velocity of the ball. The measurements are summarized below. So trial one, trial two, trial three, and trial... Trial 4. The question now, what is the percentage precision of the robot? Show the complete solution. So you just go over with the part of the video tackling this topic and sundan nyo lang yung steps and you will be able to answer this problem. So that would be all. Thank you and good luck.

So good day to all of you. This is General Physics 1, a subject in STEM strands in Senior High School. And for our lesson 2, we'll talk about accuracy and precision.

So these are our target competencies. So differentiate accuracy from precision. Differentiate random errors from systematic errors.

And estimate errors from multiple measurements of physical quantities. So let's have this concept that a good result of measurement is achieved if error made is less or limited. Whenever you are measuring something, you're happy if your measurement is correct.

So you can say that that is a good measurement because you expect it to be right and the error perhaps... Wala or kakaunti. And in measurement, gaya ng na-discuss natin in the previous lesson, measurement ay minsan hindi laging tama.

Ang measurement merong nagkakaroon ng inaccuracy, nagkakaroon ng pagkakamali sa pagme-measure. That's why this concept of accuracy and precision are considered as prime factors so that we can understand this measurement better. Is it normal for errors to happen?

Yes. Errors in measurement are unavoidable. It happens. And it is due to several factors and it cannot be random or systematic.

And it can be random or systematic depending on how measurement is made. Errors cannot be avoided. Even the greatest minds in scientific community have made...

Many, many, many errors. But in their errors, they have found the greatest invention that we enjoy in our present time. Okay, who is already familiar with darting?

Or at least familiar with darting? So imagine you are playing dart and given five darts to hit the target. You are given four chances to play.

The result of each play is illustrated below. Let's say for example, may naglalaro ng dart. At yung naglalaro ng dart, ay ganito yung naging result nya.

So for number one, so yung limang darts, ayan, dyan sya napunta. So yung target nya ay nasa gitna at scattered yung dart. Sa number two naman, ayan.

Malapit sa target. Sa number three, anlayo sa target, pero nakakonsentrate sa isang side. Tapos yung number four, medyo nakakonsentrate, tapos anlapit pa sa target.

So ano yung interpretation natin dyan kung ilalagay natin siya sa context ng accuracy and precision. Yung number one, Accuracy is poor because darts are far from each other Precision is also far because darts are far from each other Number 2 Accuracy is good because it's close to the target Right? But why is its precision poor?

Because the concentration of darts is not that much Unlike number 3 its precision is high because as you can see, the darts are almost side by side but it's far from the target, that's why its accuracy is low and number 4, its accuracy is high because it's near the target and its precision is high because all of its trials almost hit the same point of the dartboard so in that context, accuracy and precision are shown Here it is. Have you tried cooking or are you cooking but failed with the taste? Like what my father said, if it's too salty, add more sugar. If you add more, the sweetness will increase. So did you use the right measurement of the ingredients?

So if you didn't reach the desired taste, the delicious taste of what you're cooking, what could be the factors for that? for the errors or errors that uh the meeting you so there There are some factors why errors occur in every measurement. First, the kind of measuring device used.

So, the measuring device used is wrong. So, if the measuring device used is wrong, you expect that the result is erroneous. Methods in getting the measurement. It's very important that the one who measures is knowledgeable. in one, in using the measuring device and in the process per se of measurement.

Because a little mistake from the one measuring the desired measurement, it will lead to an erroneous measurement. And number three is the condition under which the measurement is made. It can be the environmental factors can affect the temperature and other factors around. So the condition has also something to deal with having an error in measurement. And there are two types of errors.

One is random error or unsystematic error. These are the errors that you don't expect and can happen instantaneously. randomly and it has no pattern. So inconsistent ito.

Example, in your first reading, you thought it might be too small then the next reading might be too large so nobody can predict random error and this cannot be avoided even scientists doing their experiments. So nung una tingin mo ang basa mo ay mababa lang and then the next reading, ang laki naman ang pagbasa mo. So What can be a factor there?

It can be the mirror used when it's wet or the lighting around it. And it is an example of a random type of error. The second one is systematic. Systematic error is consistent and repeatable error due to the kind of measuring devices as mentioned above.

It is also due to flawed experimental design. As mentioned above, If you keep on having the same error, like every time you do this procedure, you're meeting the same result or error, it means there's nothing wrong with... there's nothing wrong with...

I mean, you're the one measuring, there's nothing wrong with you. The only thing wrong is the design. or the process of measuring.

So what you have to do is you have to modify or change the way you measure the the thing that you are measuring to prevent this kind of error, the systematic error. So to minimize errors in measurement, more trials must be made. In our time, in the time of COVID-19 pandemic, Before the vaccine was made, it was being tested not just once, not just twice, but thrice or even more times before it was released to the market and given a permit to be used by people.

Why? Because in one, let's say for example, you tried it on one person and then you saw that Maganda yung result sa isang naturukan. Hindi mo pwedeng sabihin na, o pwede na tong gamitin ng general public.

Kasi compared to the general public, that one is negligible. And it can lead to results na hindi good. Kasi sa isa mo lang siya tinry.

That's why it is being tested into... thousands of volunteers so that you can see more viable results so that your measurement and your result is more solid and you are more precise more accurate and you are more far from having errors because what is best is the life of the person although we are not leaving statistics we are still doing research naapektohan o na negative side ng mga vaccines na ito. So somehow they represent the little percentage. that when the vaccine is tested, they are the little percentage that did not have a good result or what do you call that? Pag-respond to the vaccine.

So the mean or average value of these trials will be taken to represent the entire set of data. From this, the degree of accuracy and precision can be determined. So, in the context of vaccine, which is the most effective?

Which is the most accurate? Which is the lowest accuracy or the least effective? Now, let's talk about accuracy. So, accuracy, how close are you to the target?

So, if we go back to the dartboard earlier, how close is it to the target of the dartboard? So, it is the closeness or nearness. of the measurement of the accepted value.

Accuracy is expressed in terms of absolute error or percentage of error. Like this. So you have the formula AE equals absolute value of O or observed value or measured value minus the accepted value. So the accepted value is the standard value and the observed value or values are the value that was found when measuring or measured when measuring. So after finding the absolute error, you compute for the percentage error and to do that you divide Absolute error to the accepted value times 100. And for getting the percentage of accuracy, you subtract 100% to the percentage of error.

So, for you to understand these formulas and the samples, let's have this example. So, an experiment. dropped a stone from a five-story building and hit the ground, taking the time to fall of three seconds.

Based from the data collected, the experimenter was able to measure the acceleration of the stone to be 9.8 meters per second square. The actual value of the acceleration due to gravity is 9.8 meters per second square. What is the percentage of accuracy of the experiment?

So, 9.8 is... Uh... fixed value of acceleration due to gravity. But when an experiment was done on a child, he computed, so this is an observed value, he computed 9.8 meters per second. So how far or close is this to the actual value of 9.8?

So to know that, you compute for the percentage of accuracy. So first, you write the given. You have the accepted value or A.

which is 9.8 meters per second and the observed value which is O is 9.7 meters per second square. So AE equals absolute value of 0 or O minus A. Substituting the value, you have 9.7 meters per second square minus 9.8 meters per second square.

If you can see, it will result to a negative number. But since we have these parallel lines, this is called absolute value, we disregard or we get the absolute value disregarding the signs of the result, resultant value, negative 0.1. So, because it has an absolute value, it's 0.1 meters per second square. So to compute for the percentage error, you substitute the value of AE, which is 0.1 meters per second, and the value of AE, which is 9.8 meters per second squared. Dividing them gives you 1.02% times 100. Yeah.

So the result, the percentage error I mean is 1.02%. So you will then subtract that. to the 100% to get the percentage of accuracy which is 98.98%.

So, that's how close it is. or that's how accurate the actual value of gravity is. So, we can pause and go back to how we computed the AE, the percentage of error, and percentage of accuracy. Now let's talk about precision.

Precision is the agreement of several measurements made in the same way. In illustration number 3 of the dart game, the darts flocked in almost the same area. Though far from the bullseye, we can say that the measurements made are precise. So it's far from the target, it's definitely not accurate, but its precision is... almost really precise.

Precision is expressed in terms of deviation or percentage of deviation. It is expressed in terms of deviation and the formula below will help you determine the precision of one's measurement. So AD, this is AD not AE.

So AD or absolute deviation equals Absolute value of the observed value or measured value minus the mean of several measurements. I said earlier, one of the good things about measurement is that for you to be able to get a precise data, you need to have many trials because the many trials will give you consistency. You can see in these trials how consistent are the values that you are getting. So, if the values that you can see are closer, you can say that the result or the measurement is consistent.

So, after having found the AD or the absolute deviation, you get the percentage of deviation. And that is solved by dividing the AD to the... mean of several measurement times 100, and the percentage of precision is obtained by subtracting 100 from the percentage of deviation.

So, for you to understand these formulas better, let's have this example. A student is doing a laboratory experiment about falling body. He obtained three trials in measuring the time of fall.

of a ball three meters above the ground the measurements are summarized below so trial one 0.8 seconds trial two 0.79 seconds trial three 0.77 seconds the question now how precise or what is the percentage of precision of the students so the first thing that you need to do the given because is to determine the average of the three trials. Why are you getting the average of the three trials? Because you are trying to get the letter M. Min is also average.

Okay? So with that, so you add the three values of each trial, which is 0.80, 0.79, and 0.77, adding up this three and dividing it to three. you get 0.787 seconds. So that is your mean.

Now that you have your mean, you try to solve for the absolute deviation. And AD is... What do you call that? AD is O minus M or absolute value of O minus M. If you can see here, it's just one.

But because of three trials, you will do it repeatedly. So, you will have three OM. You will have three subtractions of the observed value to the mean value.

So, how is that? So, you have first trial, 0.80 minus the M. which is 0.787 quantity plus quantity of 0.787 79 seconds minus m which is 0.787 s quantity plus 0.77 for the third trial minus the m which is 0.787 divide them or perform i mean the operations so you subtract subtract subtract and after subtraction you add the measurements and divide them all by three so you get 0.011s so what do you do with that number so you now get the ad or the absolute deviation so what to do next is to find for the percentage of deviation and that is ad Divided by m times 100. So you just substitute the value.

So the value of AD, which is 0.011, and the value of m, which is 0.787 seconds, times 100, that is 1.4%. And afterwards, you get the percentage of precision, 100 minus 1.4, and you have 98. So the 98.6 is that how precise yung mga measurement na nakuha doon sa activity nung bata doon sa example natin. So pwedeng balikan yung previous slide or yung sa part ng video para mas mapag-aralan yung tungkol sa precision.

So just to reiterate, accuracy refers to how close a measurement is to a true accepted or target value. How close is it to the actual value, the most targeted, the most fixed value. Precision, when you are having reproductions or many trials, how consistent are the values you see. how close they are to each other. So that's precision.

So for my students, please do these activities. So letter A, you have the situation that Johnny and Sally perform an experiment to measure the density of aluminum. So the actual value of the density of aluminum is 2.7 grams per milliliters.

So when... John measured 2.649 grams per milliliter while Sally's measurement is 2.731 grams per milliliter. So John is lower and Sally is higher. And one look, but who among them has a closer value to the actual value of 2.7? So compute for the percentage of accuracy of both measurements.

Please show your complete solution. And the next problem, in an outdoor activity or experiment, Tokyo is testing his football robot kicking a ball and hitting the goal. She obtained four trials or four values measuring the velocity of the ball. The measurements are summarized below.

So trial one, trial two, trial three, and trial... Trial 4. The question now, what is the percentage precision of the robot? Show the complete solution.

So you just go over with the part of the video tackling this topic and sundan nyo lang yung steps and you will be able to answer this problem. So that would be all. Thank you and good luck.

Transcript for:Understanding Accuracy and Precision in Physics

Transcript for:
Understanding Accuracy and Precision in Physics