good day everybody this is mr brielle t cruz your physics one teacher for this semester for today's lesson we're going to discuss about accuracy and precision but before anything else let's have our learning objectives for this morning so first one let's differentiate accuracy from precision number two differentiate random errors from a systematic errors and lastly solve problems involving accuracy and precision i know you're thinking right now why should we even care to discuss the topic again sir it is simply because in the field of science where in measurements and many trials exist one should test whether the values obtained are considered valid or not as you all know as we go through with our lesson per hour this per semester we're going to have many experimentation and in every experimentation you're going to do trials for you to identify whether the values or data that you obtained are valid or not so let's recall the definition of accuracy when we are talking about accuracy these the closeness or nearness of the computed value to the true value so just like what you have learned when you were in grade 11 in chemistry one you learned there that if the value obtained or the present error that you are going to obtained will be less than or equal to 10 definitely you are accurate another definition for accuracy are the following hitting the target value being able to derive the true accepted and required measurement and just simply getting the it and based on the definitions that we have a while ago if we're going to put that into a real life situation for example this dart board your our target is the bull's eye so if all the dart pins will hit the bull's eye definitely we are accurate what is precision precision is number one test up how well the result agree with one another next measure up nearness and closest to the value and lastly consistency in the obtaining of the result let's put those definition in this sample diagram so if you will notice if this is the dart board and all the dart pins was placed or was targeted on that on this certain point definitely you are not accurate but you can say that you are precise because all of the dart pins are very near from each other and let's have this one so if you will notice in this dart board one of the dart pins are he hit at the target while the other two did not so therefore we can say that we are accurate but not precise in the field of science wherein you are going to test the values that you obtained you can use the test of accuracy or the percent error this is the formula for the percent error percent error is equal to the actual value minus the experimental value which is the absolute value of it over the actual value times one hundred percent if your value is more than ten percent we can say that you are inaccurate but if that is less than 10 percent you can say it is accurate but this is only just applicable for us in our school but in some universities sooner or even in your field if you're going to choose medtech or even the other courses in college you might encounter this and they might have different set of agreement per day accuracy and accuracy of the value the test of precision is known to be the deviations so when we are talking about deviation this actually the absolute deviation we're in it is equal to the x minus the x bar and the relative deviation which is actually your average absolute deviation over the mean value that you obtained times 100 if your value is more than ten percent sure and precise but if that is ten percent or less that will be precise for us again it is only applicable in our school as i said to you a while ago in our objectives we are going to differentiate random to a systematic errors so in the field of science there is no perfect result but there are reason why do you obtain or you have obtained those kind of errors in your result so when we are talking about random error this is the result unpredictable or unevitable change during the data measurements it affects the precision of the measurement example is electronic noise slight variation in temperature and uncontrollable presence of the wind another type of error is the systematic error usually come from the measuring instrument or in the design of the experiment itself here it limits the accuracy of the result aside from that we can use the percent difference when we are talking about percent difference this the measure how far apart different measurement values are from one another it is an indication of the precision so for you to solve for it this is the formula for the percent difference percent difference is equal to the measurement one minus measurement two divided by the measurement one plus measurement two over two times one hundred this is used for you to determine whether the values that you obtain the two values that you obtained is precise for this example problem for percent difference you will see the complete solution of the answer on the next slide first up let's try to solve the percent different sample problem but before that let's read so two trials were performed in an experiment to determine the latent heat of vaporization of water at 100 degrees celsius the values of lb of water is obtained where 5 3 2 calories per gram and pipe 36 calories per gram find the percent difference of the value so x1 is pipe32 and our x2 is 536 using the formula per percent difference which is x1 minus x2 the absolute value divided by one plus x two divided by two times one hundred let's substitute it so pipe three two minus pipe three is six we will get negative value here which is negative four divided by pipe three two plus pipe three six divided by two then multiply it by one hundred we will get zero point seventy per percent so therefore there is a zero point seventy four percent of percent difference between the two values obtained in the experiment let's try to solve the present difference sample problem but before that let's read let's solve sample number two using microsoft excel so for example number two let's reiterate the problem the true value for the volume the rubber ball is 50 cc is the measure accurate precise or both so here i will be showing how to support the average and the absolute deviation so i have written here the trials that we have one two three four so we have four trials and the value of the volume for each trial so we need to solve for the average volume so how do we do that so right here equals then average the word average open close parenthesis then drag the value that you have here then close parenthesis then press enter so there you have it so 50 point 14. now how do we solve for the absolute deviation so for the absolute deviation as we all know this is the difference between the average volume minus the value obtained for each trial so you just write equals then 50 point 14 minus l8 then press equals so we have 0.62 for the first trial then let's drag it here to the point trial then you have the value for the absolute deviation but since this absolute deviation we are going to disregard the negative sign in getting the average absolute deviation since we're done already solving for the absolute deviation value and as we all know for getting the average absolute deviation what are we going to do is to copy the values that we have here for trials 1 to 4 for the absolute deviation so let's copy the values so right click then copy place it on the other side then paste values so with that as you all as you can see we're just going to remove the negative sign for trial 2 and trial 4 so that we can solve for the absolute absolute deviation so with that then let's remove then below let's try to solve for the average absolute deviation so equals then type the word average then open close parenthesis then drag from this 08 up to o 11 then close parenthesis then press enter then you will see the answer will be 0.90 which i place it here on this part so 0.90 so let's just increase the decimal places oops yeah since we computed already for the average volume together with the average absolute deviation we can now solve for the precision of the values that we have so for the precision we're going to use the absolute average deviation together with the mean value so using the relative deviation formula which is average absolute deviation divided by the mean value times 100 so using the value so 0.90 divided by 50.14 times 100 you will get 1.79 percent which is precise next for the percent error you're going to use the actual value for the volume which is 50 and the experimental value which is 50.14 so using the formula av minus ev divided by av times 100 so substituting it so 50 minus 50.14 divided by 50 times 100 you will get 0.28 therefore it is accurate for the interpretation we can say therefore the experimenters are both accurate and precise based on the data they obtained from the experiment so two trials were performed in an experiment to determine the latent