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Uncertainty and Error in Lab Measurement

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hello AP Physics this is mrs. Comstock and today we're going to talk about uncertainty and error in lab measurements measurement is at the heart of Science in order to do science we must be able to measure quantities such as time distance and mass as famous physicist Williams said when you cannot measure your knowledge is of a meager and unsatisfactory kind  two issues must be confronted when / forming measurement  the possibility of air during the measurement and some unavoidable uncertainty in the measurement video we will learn about sources of measurement error how to identify and avoid them will also learn about measurement uncertainty asep but related topic that is Central to our success in the science laboratory and lastly we all learn how to determine the amount of uncertainty in a measurement the word air is used to mean many different things and its use in science can sometimes be confusing the term air candy you mean mistake or the difference between two values sometimes the words error and uncertainty are used interchangeably use the term heir to mean the difference between a measured value and a true or the actual value  here's an example say you'd like to measure the number of people attending a concert standing side-by-side in an auditorium you also have no means of counting every person so you come up clever idea  you first noticed that the floor is covered with large tiles and there are 20 tiles wide by 40 tiles so you determine their 800 tiles with three people standing on each tile you determine if there are 2400 people in the room then at the end of the concert you talk to the ticket Sellers and find out that they have a MIT admitted 2450 people into the auditorium the swimming they did not make any mistakes your measurement is off by 50 people  error can be expressed as the absolute value of the difference between a measurement and the actual value we call this absolute error  in a case we would say that the absolute error in our measurement was 50 people  air can also be expressed as a purse of the actual or real value we call this relative error we can calculate relative error according to the formula shown for the case of the relative error of our measurement would have come out 2.13% note that the concept of air as we use it here makes sense only in cases where the actual value is known we will use the term accuracy to mean the relative error in a measurement the accuracy of a measurement is how close it is to the actual value  what type of bear that can affect the measurements it's called systematic error systematic errors are ones that consistently cause the measured value to be either large or too small systematic errors can be caused by faulty equipment such as miscalibrated balances or inaccurate meter sticks or stop watches other systematic errors occur when he quipment is used incorrectly like reading from the wrong end of a meter stick forgetting to subtract the way the container when finding the mass of a liquid or converting units in correctly  an example of this kind of air is shown notice what's a wood block being measured is lined up with the left edge of the ruler but the zero reference line is not at the end unless we notice this all measurements done in this way will yield measured values lower than the actual length no matter how many times we repeat the measurement an example of systematic error we must be clever and careful to think of sources of systematic error considered timing a running race where the person timing the race stands at the finish line starting the watch when they hear the starting gun and stopping the wash when the runner crosses Finish Line  the time it takes for the timer to react to the sound of the gun as well as the delay for the sound to travel from the gun to the timer will always yield the time on the stopwatch to be less than the actual time of the race both are examples of system errors  often systematic errors can be eliminated if you know they exist in some cases it can be very difficult to I systematic errors in these cases the errors often go undiscovered until another measurement is made using a different measuring we can never be sure that our experiments are completely free from systematic errors the best way to add confidence to our measurements devise an experiment to measure the same quantity by a completely different method that is unlikely to have the same air  let's consider another force of air in the times recorded in the running race described earlier no matter how careful the time or was they would never be able to stop the watch at Zach instant the runner cross the line sometimes they would stop the watch slightly before the runner reach the line sometimes slightly after this is example of a source of random air random is when variations in the measurements occur without a predictable pattern if peanut measurements are made random errors cause the measured value to Ferry sometimes above and sometimes below the actual measured value because of this random error causes uncertainty in measurements along with reaction time another source of random errors comes from reading the scale on a measurement tool that looks like a thermometer or a meter stick since the actual value will usually fall in between two marks on the scale the reader has to estimate the actual value sometimes their estimate will be too high other times too low this is another example of random error causing on we can determine how much random air are measurements half by repeating the measurements many times if our results are or nearly the same this indicates a small amount of random error if on the other hand are results are different each time we measure the same thing we must have random air affecting the results random errors can be reduced but never eliminated random errors do not always prevent our measurements from being useful but it does contribute to measurement uncertainty  whenever you or anyone else makes a measure we can never be certain that the result that the result is exactly correct there is always some difference between the measured value and the app value no matter how careful you are no matter how exotic the equipment and how intelligent the operator there is always some uncertainty associated any measurement what's more if we use a measured value to make a calculation the results of the calculation will also not be exactly correct they will also have some uncertainty associated with them this is an unavoidable part of science  measurement uncertainty need not prevent measurements from being if we can quantify the uncertainty for a measurement that is if we can determine the amount of uncertainty we can still use the measurement with confidence we can do this by specifying a range of values between which we are absolutely certain the true value of our measurement lies the term uncertainty implies lack of knowledge but when we describe a measurement as a range of values we are really saying that we are certain that the actual value of the measurement does lie within this range  let's begin by CNY all Unser is inherent in all measurement let's look at two types of measurement devices analog and digital measuring devices turn the vices fall into one of these two categories Analog Devices like the meter stick shown have a printed scale with graduation lines numbers printed next to them a digital measuring instrument have half electronic digital displays that show numbers or did to see how uncertainty creeps into analog measurement look at the photo of the meterstick we see that the length the object might fall between the graduation marks on the scale  since we can never see exactly where the object falls on the graduation on an analog measuring device we will always have some uncertainty about the value of the measurement things are things are no better we use a digital measuring device All Digital measuring devices are limited to a certain number of digits on the display the device must tell the measurement to the nearest decimal to display it this rounding process introduces uncertainty because when we read the device we can't tell what numbers were for rounding  since all measuring devices are either analog or digital all measurements fall prey to these problems to be able to measurements effectively in confidently we need to be able to express the amount of uncertainty in our measurements  as we just we can never know the exact value of a measurement but when we measure something we can determine a range of values between which we are certain the truth nuke lies in this section will learn a way to estimate the amount of uncertainty in a reading taken from an analog scale such as a meter stick spring scale or triple beam balance look at the picture of the spring scale which measures force in Newtons notice at the small marks and 8.5 Newtons we can't tell exactly what the scale reads but we can see that there can be no question that the scale reading is between 4.5 Newtons and 5.5 Newtons we can say with absolute certainty that the scale reading is somewhere between these two we will Express this range of values in the form shown when riding the range in this for Beck's is the measured value in Delta X is the absolute uncertainty or the amount of uncertainty of the measurement or we can think of it this way X is how much we think the measurement is in Delta X is the maximum amount by which we think the measurement can be off using the example of the spring scale we should say that the force is 5.0 plus or minus 5 Newtons  when reading an analog instrument the user must be the judge of what range he or she confident the actual value of the measurement lies there is no absolute rule that determines what range of certainty to use it depends on the of the credit scale and how clearly the user can see where the reading is on that scale we can also measure the amount of uncertainty into measurements using a ratio called relative uncertainty uncertainty is the amount of uncertainty divided by the total amount of the measurement or using the variables named in the earlier section relative uncertainty is equal to Delta x divided by X usually will Express relative uncertainty as a percent so after you divide x 100  we will use the term Precision to mean the amount of relative in uncertainty in a measurement the spring scale mentioned earlier had an uncertainty of 5.0 plus or minus .5 so the relative uncertainty can be calculated by taking .5 Newtons divided by 5 Newtons times 100 which equals 10% because of this play on a digital instrument shows clearly the numbers of the measurement it seemed it may seem like they are less prone to uncertainty than analog measurements however All Digital instruments have inherent uncertainty due to a limited number of digits that can be shown on the display here is an example the spice shown is rounded to the nearest gram the actual unrounded value could be anywhere between 242.5 and 243.5 grams we say that the digital scale has a resolution of one gram we can use the method mentioned earlier to find the uncertainty but there is a shortcut We Know by looking at the play that 243 is the actual scale reading in addition we know that the maximum amount by which the scale reading see off is half of the value of the last decimal place shown if it were off by more than that the reading would be rounded to show a different value in this case the last decimal place shown is the grams decimal place so the maximum by which we could be off is a half a gram or .5 grams so the uncertainty for this reading should be 243 plus or minus .5 grams  we hope this video is helped you can also find the complete packet from which this video made at the site listed have a great day

Uploaded by Nicole Comstock.

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Uncertainty and Error in Lab Measurement

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