Accuracy vs Precision in AP Physics

Accuracy is how close a measurement is to the accepted value. Precision is how close repeated measurements are to each other. Judging accuracy needs a known reference value; judging precision needs only your own data. That is why readings can be tightly clustered and badly wrong at once.

This pair is experimental-design vocabulary rather than unit content, and neither term is defined in the AP Physics 1 Course and Exam Description effective fall 2024. No learning objective or essential knowledge statement in the course framework uses the word accuracy or precision. The word precision appears once in the whole document, in the Laboratory Investigations section, in a note that electronic force sensors tend to have much more precision and accuracy than spring scales; the identical sentence is the only occurrence of the word in the AP Physics C: Mechanics description, and the word does not appear in the AP Physics 2 or AP Physics C: Electricity and Magnetism descriptions. The word accuracy appears only in prose: the front matter on scoring standards, the Laboratory Investigations note on checking the accuracy of student work, a teaching-strategy example, and the Instructional Approaches discussion of working within the level of accuracy needed for the course. The CED's own term for this material is experimental uncertainty. It sits under Science Practice 3, Scientific Questioning and Argumentation, whose discussion states that scientific instruments do not produce exact measurements and suggests designing a second experiment to check for consistency, and under skill 3.A, create experimental procedures that are appropriate for a given scientific question, whose listed questions include what steps can be taken to decrease the uncertainty in the measurements and data. It is assessed on the third free-response question, Experimental Design and Analysis, carrying skills 1.B, 2.B, 2.D and 3.A for 10 points with a suggested time of 25 to 30 minutes; the CED's published scoring guideline for its sample of that question awards a point for a reasonable method of reducing experimental uncertainty either by taking several measurements at the same depth or height, or at least one measurement at several depths or heights. The task verb Calculate requires correct labeling of units and significant figures.

The distinction, stated once

Accuracy compares your measurement with the accepted value. Precision compares your measurements with each other.

That single sentence carries the difference, and the reason it matters is that the two are judged from different information:

To decide whether a result is accurate you need something external, an accepted value obtained some other way. Your own data cannot tell you.
To decide whether a set of results is precise you need nothing but the set itself. Look at the spread.

So the dangerous case is a tight cluster in the wrong place. Five readings of $9.21$ , $9.22$ , $9.20$ , $9.23$ and $9.19\ \text{m/s}^2$ for the acceleration due to gravity have a spread of only $0.04$ , which looks like a well-run experiment, and a mean that is 6 percent below the value on the equation sheet. Repeating that measurement a hundred more times would not reveal the problem, because repetition tests precision and nothing else.

The two also respond to different fixes. Averaging more repeats shrinks random scatter and therefore improves precision. It does nothing whatsoever to a systematic offset, so it cannot improve accuracy. To catch an accuracy problem you have to change something about the method, which is exactly what the AP Physics 1 CED suggests in its Science Practice 3 discussion: one step may be designing a second experiment to determine the same quantity and then checking for consistency across the two measurements.

Before going further, one thing worth knowing about these two words in an AP context, because it changes how you should answer a question that seems to be about them: the AP Physics 1 CED does not define either term. Section four below sets out what the document actually says. The experimental uncertainty glossary entry covers the language the CED does use.

Accuracy vs precision, side by side

	Accuracy	Precision
What it describes	How close a measurement is to the accepted value	How close repeated measurements are to each other, and how finely the instrument resolves
What you need to judge it	An accepted value from an independent source	Only your own data set
Type of error it tracks	Systematic error, a consistent offset	Random error, scatter
Improved by	Calibrating, removing an offset, or changing the method	Repeating and averaging, or using a finer instrument
Effect of taking more repeats	None, if the error is systematic	It improves
Detected by	Comparing against a second, different method	Comparing repeats of the same method
Usually quantified by	Percent error, which requires an accepted value	The spread of the data, reported as an uncertainty range
How it shows up in a written answer	A stated comparison with a reference value	The number of significant figures and a plus-or-minus range
Can be good while the other is bad	Yes: scattered readings whose mean happens to land on the accepted value	Yes: a tight cluster in the wrong place
Defined in the AP Physics 1 CED	No	No
The term the CED uses instead	Experimental uncertainty, and sources of uncertainty and error	The same terms

The row on repeats is the one that decides most exam answers. A method for reducing random error is not a method for improving accuracy, and a question that asks you to reduce experimental uncertainty is asking about the spread, so "repeat the measurement and average" earns the point while "be more careful" does not.

The case that separates them: four data sets, one target

Four groups measure the acceleration due to gravity five times each. Take the accepted value to be the $9.8\ \text{m/s}^2$ printed in the AP Physics 1 Table of Information.

Group	Readings ( $\text{m/s}^2$ )	Mean	Spread	Percent error of the mean
A	9.79, 9.81, 9.80, 9.82, 9.78	9.80	0.04	0.0 percent
B	9.21, 9.22, 9.20, 9.23, 9.19	9.21	0.04	6.0 percent low
C	9.2, 10.4, 9.5, 10.1, 9.8	9.80	1.2	0.0 percent
D	8.6, 9.1, 10.6, 8.9, 10.0	9.44	2.0	3.7 percent low

Read the table as a two-by-two grid and every combination is present:

A is accurate and precise. Tight, and centred on the accepted value.
B is precise and not accurate. Its spread is $0.04$ , identical to group A's, and its standard deviation is identical too, at $0.016$ . Every measure of precision says B is as good as A. The mean is wrong by 6 percent.
C is accurate and not precise. The spread is thirty times A's, and the mean lands exactly on $9.80$ . That is what averaging does to random scatter: it cancels, given enough readings.
D is neither. Wide and off-centre.

Three things follow, and they are the whole practical content of the distinction.

Precision is visible from the inside; accuracy is not. Group B could compute its spread, its standard deviation and its uncertainty range, and every number would look excellent. Nothing internal to those five readings reveals the 6 percent problem. Only the comparison with $9.8$ does, and that number came from outside the experiment.

Averaging fixes one and not the other. C's mean is right because random errors sit on both sides of the true value and cancel. B's mean is wrong because its error sits on one side every time, so it survives any number of repeats.

A precise-and-wrong result is worse than an imprecise one, because it invites confidence. Group D can see that something is unstable. Group B cannot. The CED's own remedy is the right one: run a second, different experiment for the same quantity and check the two against each other.

What the AP Physics 1 CED actually says about these two words

This is the part no other page on this pair will tell you, and it is worth knowing before you write "accuracy" in a free-response answer.

Neither term is defined anywhere in the AP Physics 1 course framework. There is no learning objective and no essential knowledge statement about accuracy or precision. The words appear only in surrounding prose.

The word precision appears exactly once in the whole document, in the Laboratory Investigations section, in a note about equipment: electronic force sensors tend to have much more precision and accuracy than spring scales. That is the sentence. It uses both words as ordinary English, without defining either.

The word accuracy appears in a handful of places, none of them a definition: in the front matter, about maintaining the accuracy of the scoring standards; in the Laboratory Investigations section, about students using instant feedback to check the accuracy of their work; in the equipment note above; in a teaching-strategy example; and in the Instructional Approaches discussion of modelling, about obtaining an answer that is within the level of accuracy needed for the course.

The same holds across the other descriptions. The AP Physics C: Mechanics CED contains the word precision once, in the identical equipment sentence about electronic force sensors. The AP Physics 2 and AP Physics C: Electricity and Magnetism descriptions do not contain the word precision at all.

So what should you conclude? Not that the ideas are absent. The CED asks for exactly this reasoning under a different name, and the name is uncertainty. Two consequences for how you answer:

Do not expect a question that asks you to define accuracy or precision or to distinguish them as vocabulary. Nothing in the framework supports one.
Do expect questions about reducing experimental uncertainty and about identifying sources of uncertainty and error. Those phrases are in the document, in the science practices and in the published scoring guidelines, and they are where this material is actually assessed. The next section sets out what the CED asks for.

One related point on the accepted value itself, since accuracy depends on having one. A Topic 1.3 boundary statement says that for all situations in which a numerical quantity is required for $g$ , the value $g \approx 10\ \text{m/s}^2$ will be used, and then adds that students will not be penalized for correctly using the more precise commonly accepted values of $g = 9.81\ \text{m/s}^2$ or $g = 9.8\ \text{m/s}^2$ . The Table of Information prints $9.8$ . So even the reference value has a choice in it, and is g 9.8 or 10 works through what that choice does to a percent error.

What the CED asks for instead: reducing experimental uncertainty

Science Practice 3 is where this lives. Its heading is Scientific Questioning and Argumentation, and its description is to describe experimental procedures, analyze data, and support claims. The discussion says it is important that students understand that scientific instruments do not produce exact measurements and learn what steps they can take to decrease uncertainty, and adds that one step may be designing a second experiment to determine the same quantity and then checking for consistency across the two measurements. Elsewhere it notes that class discussions can reveal issues of measurement uncertainty and assumptions in data collection.

Under skill 3.A, create experimental procedures that are appropriate for a given scientific question, the CED lists the questions to ask students, and four of them are this material directly:

What possible errors need to be addressed before data collection?
What steps can be taken to decrease the uncertainty in the measurements and data?
What changes can be made to observations and measurements to refine the data?
How can a second experiment be designed to answer the same scientific question and check for consistency?

The sample activity attached to that skill is to have students list the common sources of uncertainty and error in an experiment designed to find the rotational inertia of a bicycle wheel, then identify or describe the manner in which each source would affect the results of the experiment. That last clause is the accuracy-and-precision distinction without the vocabulary: some sources shift the result one way every time, and some scatter it.

This is assessed on the third free-response question, Experimental Design and Analysis, which carries skills 1.B, 2.B, 2.D and 3.A, is worth 10 points, and has a suggested time of 25 to 30 minutes. The CED's own sample of that question asks students to briefly describe a method to reduce experimental uncertainty for the measured quantities, and its published scoring guideline awards the point for a reasonable method of reducing experimental uncertainty either by taking several pressure measurements at the same depth or height, or at least one pressure measurement at several depths or heights.

Read that scoring note closely, because it names two different moves:

Several measurements of the same thing attacks random scatter. This is a precision move.
Measurements at several different values lets you plot a graph and use its slope, which attacks a constant offset as well. This is an accuracy move, and worked example three shows why: a slope is blind to a systematic offset that ruins every individual reading.

The two are both worth the point, and they are not the same idea. Linearization is the technique behind the second.

How precision gets written down: significant figures

Precision is not only a property of a data set; it is something your written answer claims. The digits you print are a statement about how well you know the quantity.

The CED makes this part of the answer rather than a stylistic preference. The task verb Calculate is defined as performing mathematical steps to arrive at a final answer, including algebraic expressions, properly substituted numbers, and correct labeling of units and significant figures. So a number with too many digits is claiming a precision the measurement does not support, and a number with too few is discarding information you had.

The two rules worth having, from significant figures:

A product or a quotient keeps the fewest significant figures of its inputs.
A sum or a difference keeps the fewest decimal places.

And the trap: significant figures report precision and say nothing about accuracy. Writing $9.21000\ \text{m/s}^2$ does not make group B's result any less wrong; it makes the wrongness more confidently stated. A result can be quoted to five figures and be 6 percent off.

One practical technique that increases precision without any better equipment, and it is the reason pendulum labs time ten swings rather than one. Reaction time in starting and stopping a stopwatch is a fixed uncertainty of a couple of tenths of a second, and it does not grow when you time a longer interval. So measure a large multiple and divide:

Time one oscillation of about $1.43\ \text{s}$ with an uncertainty near $0.2\ \text{s}$ and the relative uncertainty is about 14 percent.
Time ten oscillations, get $14.32\ \text{s}$ with the same $0.2\ \text{s}$ uncertainty, divide by ten, and the period is $1.432\ \text{s}$ with an uncertainty near $0.02\ \text{s}$ , about 1.4 percent.

Same stopwatch, same hands, ten times the precision, and this is the kind of move skill 3.A's question about refining measurements is asking for. Worked example two follows it through to a value of $g$ .

Where it costs a mark

Offering "repeat the measurement and average" as a way to improve accuracy. Averaging cancels random scatter. A systematic offset survives it untouched.
Offering "be more careful" or "use better equipment" with no mechanism. The CED's scoring guideline for reducing experimental uncertainty rewards a specific procedure: several measurements at the same value, or measurements at several different values. Name the measurement and name what you will repeat or vary.
Claiming a result is accurate on the strength of a small spread. A small spread is precision. Accuracy needs a comparison with an independently known value.
Quoting more significant figures than the data supports. The task verb Calculate requires correct labeling of units and significant figures, so this is a scored item rather than a style note.
Computing a percent error with no accepted value. Percent error needs a reference. Comparing two of your own measurements gives a percent difference, which is a different quantity and answers a different question.
Using a single data point when the question asked for a graph. The Experimental Design and Analysis question asks you to plot a graph and analyse its slope or intercept precisely because that method resists a constant offset in every reading. A single point cannot.
Treating a stated uncertainty as an accusation of carelessness. An uncertainty is a property of a measurement, and the CED says outright that scientific instruments do not produce exact measurements. A lab write-up with no uncertainty discussion has not been careful, it has been silent.
Writing about accuracy and precision as defined AP vocabulary. Neither term is defined in the AP Physics 1 course framework. Say what you mean instead: that the readings agree closely with each other, or that the mean sits above the accepted value. Both statements score; the labels alone may not.
Assuming a finer instrument scale fixes everything. A scale that reads to $0.001$ can still be miscalibrated, which is precision without accuracy, exactly group B.

When they coincide, and how each gets a number

The two travel together in the ordinary case, which is why the distinction goes unnoticed. A well-calibrated instrument used carefully on a well-designed procedure gives results that are both precise and accurate, and then the spread of your data really is a fair guide to how far you are from the truth. That is group A, and most of a school lab course.

They come apart in three recognisable situations:

A calibration offset. A zero error on a force sensor, a ruler with a worn end, a scale that reads high by a fixed amount. Every reading is shifted the same way, so precision is untouched and accuracy is gone.
A flaw in the model rather than the instrument. Neglecting friction, treating a real pulley as massless, assuming air resistance is negligible when it is not. The measurements are fine and the quantity you extracted from them is not. The Instructional Approaches section of the CED is explicit that these simplifications are chosen to obtain an answer that is within the level of accuracy needed for the course, and that students should understand they are using a simplified model.
A reference value that is itself a choice. Comparing against $9.8$ or against $10$ changes a percent error by 2 percent before you have measured anything.

How each gets a number. Precision is reported as a spread: a range, a plus-or-minus figure, or the number of significant figures you print. Accuracy is reported as a percent error, which needs the accepted value:

\text{percent error} = \frac{\lvert \text{measured} - \text{accepted} \rvert}{\text{accepted}} \times 100

Note that no percent-error formula is printed on the AP Physics 1 equation sheet. It is not in the Table of Information and there is no uncertainty section on the sheet at all, so if a question wants it you write it from the definition. Percent error has the details, and the distinction from percent difference, which compares two measurements to each other and needs no reference value.

The full AP Physics 1 sheet is here. For a topic where this reasoning is actually examined, the CED's sample Experimental Design and Analysis question uses fluid pressure, so Topic 8.2 and the fluids practice set are the closest content, and worked example three below reconstructs that experiment.

Four groups, four verdicts

Four groups each measure the acceleration due to gravity five times. Group A gets 9.79, 9.81, 9.80, 9.82, 9.78. Group B gets 9.21, 9.22, 9.20, 9.23, 9.19. Group C gets 9.2, 10.4, 9.5, 10.1, 9.8. Group D gets 8.6, 9.1, 10.6, 8.9, 10.0, all in $\text{m/s}^2$ . Find each mean, each spread and each percent error against the accepted value $9.8\ \text{m/s}^2$ , then classify each group and say what each should do next.

Group A. Sum $= 9.79 + 9.81 + 9.80 + 9.82 + 9.78 = 49.00$ , so the mean is $49.00/5 = 9.80\ \text{m/s}^2$ . Spread $= 9.82 - 9.78 = 0.04$ . Percent error $= \lvert 9.80 - 9.8 \rvert / 9.8 \times 100 = 0.0$ percent.
Group B. Sum $= 9.21 + 9.22 + 9.20 + 9.23 + 9.19 = 46.05$ , so the mean is $46.05/5 = 9.21\ \text{m/s}^2$ . Spread $= 9.23 - 9.19 = 0.04$ , identical to group A's. Percent error $= \lvert 9.21 - 9.8 \rvert / 9.8 \times 100 = 6.0$ percent low.
Group C. Sum $= 9.2 + 10.4 + 9.5 + 10.1 + 9.8 = 49.0$ , so the mean is $9.80\ \text{m/s}^2$ . Spread $= 10.4 - 9.2 = 1.2$ , thirty times A's. Percent error $= 0.0$ percent.
Group D. Sum $= 8.6 + 9.1 + 10.6 + 8.9 + 10.0 = 47.2$ , so the mean is $47.2/5 = 9.44\ \text{m/s}^2$ . Spread $= 10.6 - 8.6 = 2.0$ . Percent error $= \lvert 9.44 - 9.8 \rvert / 9.8 \times 100 = 3.7$ percent low.
Now compare A with B, which is the pair that carries the point. Their spreads are identical, at 0.04, and so are their standard deviations, at 0.016. Every internal measure of quality is the same. A is on the accepted value and B is 6 percent below it, and nothing inside B's five numbers could have told you.
Compare A with C. C's mean is exactly right and its spread is thirty times larger. Its errors scattered on both sides and cancelled in the mean, which is what random error does when you average enough of it.
Classify. A: accurate and precise. B: precise, not accurate. C: accurate, not precise. D: neither.
What each should do next. A: nothing, report the result with its uncertainty. C: take more readings, since averaging is the correct response to scatter, and consider a finer instrument. D: the same, but the size of the scatter suggests something in the procedure is unstable, so look for the source before adding readings. B: adding readings is useless. Check for a calibration offset and, following the CED's Science Practice 3 suggestion, design a second experiment for the same quantity by a different method and compare the two.
A closing check on the arithmetic: A and C have the same sum, 49.0, and therefore the same mean. Two very different data sets, one mean, which is the shortest possible statement that a mean does not report precision.

Means 9.80, 9.21, 9.80 and 9.44 $\text{m/s}^2$ ; spreads 0.04, 0.04, 1.2 and 2.0; percent errors 0.0, 6.0, 0.0 and 3.7 percent. A is accurate and precise, B precise but not accurate, C accurate but not precise, D neither. B is the dangerous one: its precision is identical to A's, so no amount of repeating will expose its 6 percent systematic offset, and only a second method will.

Timing ten swings instead of one

A simple pendulum of length $0.510\ \text{m}$ is timed with a stopwatch whose reading is uncertain by about $0.2\ \text{s}$ because of reaction time. One student times a single oscillation and gets $1.43\ \text{s}$ . Another times ten oscillations and gets $14.32\ \text{s}$ . Find the period and its relative uncertainty in each case, then find $g$ from the ten-oscillation measurement and its percent error against $9.8\ \text{m/s}^2$ .

Single oscillation. Period $T = 1.43\ \text{s}$ , with an uncertainty of $0.2\ \text{s}$ . Relative uncertainty $= 0.2 / 1.43 = 0.14$ , about 14 percent.
Ten oscillations. Total time $14.32\ \text{s}$ , with the same $0.2\ \text{s}$ uncertainty, because the reaction time does not grow with the interval. Period $T = 14.32 / 10 = 1.432\ \text{s}$ , and the uncertainty divides by ten as well: $0.2 / 10 = 0.02\ \text{s}$ . Relative uncertainty $= 0.02 / 1.432 = 0.014$ , about 1.4 percent.
So the second method is ten times as precise with the same equipment and the same reflexes. Note also that the extra digit in $1.432$ is now earned: the first student could not honestly write a third decimal place.
Find $g$ . The printed relation for a pendulum is $T_p = 2\pi\sqrt{\ell / g}$ , which rearranges to $g = \frac{4\pi^2 \ell}{T^2}$ .
Substitute: $4\pi^2 = 39.478$ , and $4\pi^2 \ell = (39.478)(0.510) = 20.134$ . With $T^2 = (1.432)^2 = 2.0506$ , $g = 20.134 / 2.0506 = 9.8185\ \text{m/s}^2$ , so $9.82\ \text{m/s}^2$ to three significant figures.
Percent error: $\lvert 9.8185 - 9.8 \rvert / 9.8 \times 100 = 0.19$ percent.
Now propagate the precision. Because $g$ depends on $1/T^2$ , a relative uncertainty in $T$ roughly doubles when it reaches $g$ . From the ten-oscillation timing, $2(1.4) = 2.8$ percent, so $g = 9.82 \pm 0.27\ \text{m/s}^2$ . From the single-oscillation timing, $2(14) = 28$ percent, so $g = 9.85 \pm 2.8\ \text{m/s}^2$ , a range running from about $7.1$ to about $12.6$ .
Read the two results side by side. Both means are close to $9.8$ , so both students were accurate, and only one of them can demonstrate it. The single-oscillation result is consistent with $9.8$ and equally consistent with $12$ , which makes it nearly useless as evidence. Precision is what turns a measurement into an argument.
One accuracy caution this example does not fix. Timing ten swings does nothing about a systematic problem, such as a length measured to the bottom of the bob instead of to its centre of mass, or a swing amplitude too large for the model behind $T_p = 2\pi\sqrt{\ell/g}$ . Those would shift every trial the same way, and only a change of method or a second experiment would show it.

Single oscillation: $T = 1.43\ \text{s}$ , about 14 percent relative uncertainty. Ten oscillations: $T = 1.432\ \text{s}$ , about 1.4 percent. From the second, $g = 9.82\ \text{m/s}^2$ , a percent error of 0.19 percent, and propagating the timing precision through $g \propto 1/T^2$ gives $9.82 \pm 0.27\ \text{m/s}^2$ against $9.85 \pm 2.7\ \text{m/s}^2$ from the single swing. Ten times the precision, same stopwatch.

A slope survives an offset that ruins every reading

Students determine the density of a liquid by lowering a pressure sensor to five depths and recording the absolute pressure, using $P = P_0 + \rho g h$ with $P_0 = 1.0 \times 10^5\ \text{Pa}$ and $g = 9.8\ \text{m/s}^2$ . Their sensor has an unnoticed systematic offset that adds $500\ \text{Pa}$ to every reading. Their data are $101{,}480$ , $102{,}460$ , $103{,}440$ , $104{,}420$ and $105{,}400\ \text{Pa}$ at depths of $0.10$ , $0.20$ , $0.30$ , $0.40$ and $0.50\ \text{m}$ . Find the density from the slope of a graph of $P$ against $h$ , then find it from single readings at $0.10\ \text{m}$ and at $0.50\ \text{m}$ , and compare.

Set out the model. $P = P_0 + \rho g h$ is a straight line of $P$ against $h$ with slope $\rho g$ and intercept $P_0$ , which is why the CED's own sample of this question asks for a linear graph.
Slope from the first and last points: $\text{slope} = \frac{105{,}400 - 101{,}480}{0.50 - 0.10} = \frac{3920\ \text{Pa}}{0.40\ \text{m}} = 9800\ \text{Pa/m}$ .
Check the linearity before trusting it. Consecutive readings differ by $980\ \text{Pa}$ for each $0.10\ \text{m}$ step, five times over, so the points lie exactly on a line and the slope is well determined.
Density from the slope: $\rho = \frac{\text{slope}}{g} = \frac{9800\ \text{Pa/m}}{9.8\ \text{m/s}^2} = 1000\ \text{kg/m}^3$ . Correct, to every digit, even though not one of the five pressure readings was correct.
Why it survived. The $500\ \text{Pa}$ offset is added identically to every reading, so it shifts the whole line up without tilting it. A slope is a difference of readings divided by a difference of depths, and the offset cancels in the subtraction. What it does corrupt is the intercept, which comes out as $100{,}500\ \text{Pa}$ instead of $100{,}000\ \text{Pa}$ .
Now the single-point route at $h = 0.10\ \text{m}$ , assuming the stated $P_0 = 1.0 \times 10^5\ \text{Pa}$ : $\rho = \frac{P - P_0}{gh} = \frac{101{,}480 - 100{,}000}{(9.8)(0.10)} = \frac{1480}{0.98} = 1510\ \text{kg/m}^3$ . That is 51 percent high.
Single point at $h = 0.50\ \text{m}$ : $\rho = \frac{105{,}400 - 100{,}000}{(9.8)(0.50)} = \frac{5400}{4.9} = 1102\ \text{kg/m}^3$ , 10 percent high. Better, because the same fixed $500\ \text{Pa}$ error is a smaller fraction of a larger measured difference, and worse than useless as a check, because it looks plausible.
Collect the three answers: $1000$ , $1510$ and $1102\ \text{kg/m}^3$ , from the same five readings. The precision of the data was excellent throughout, with the points lying perfectly on a line. Precision told you nothing about which of the three numbers to trust.
This is why the published scoring guideline for the CED's sample question credits taking at least one pressure measurement at several depths as a way of reducing experimental uncertainty, alongside repeating measurements at a single depth. The repeating attacks scatter; the several depths attack the offset.

From the slope, $\rho =$ 1000 kg/m $^3$ , exactly right despite a $500\ \text{Pa}$ error in every reading, because a constant offset shifts the line without changing its gradient. From a single reading at $0.10\ \text{m}$ , 1510 kg/m $^3$ , 51 percent high; at $0.50\ \text{m}$ , 1102 kg/m $^3$ , 10 percent high. The offset does show up in the intercept, which comes out as $100{,}500\ \text{Pa}$ rather than $100{,}000\ \text{Pa}$ .

Frequently asked questions

What is the difference between accuracy and precision?

Accuracy is how close a measurement is to the accepted value. Precision is how close repeated measurements are to each other, and how finely the instrument resolves. The practical difference is what you need in order to judge each one: accuracy requires an accepted value obtained independently, while precision can be judged from your own data alone by looking at the spread. That is why a set of readings can be tightly clustered and badly wrong at the same time. Five readings of the acceleration due to gravity clustered within 0.04 of 9.21 metres per second squared are precise and are 6 percent below the accepted 9.8.

Does the AP Physics 1 CED define accuracy and precision?

No. Neither term appears in any learning objective or essential knowledge statement of the AP Physics 1 course framework. The word precision occurs exactly once in the whole document, in the Laboratory Investigations section, in a note saying that electronic force sensors tend to have much more precision and accuracy than spring scales. The word accuracy occurs in a few places of surrounding prose, none of them a definition. The same equipment sentence is the only occurrence of precision in the AP Physics C: Mechanics description, and the AP Physics 2 and AP Physics C: Electricity and Magnetism descriptions do not contain the word at all. What the CED does ask about, repeatedly, is experimental uncertainty.

Can a measurement be precise but not accurate?

Yes, and it is the most dangerous combination, because nothing inside your own data reveals it. Precision means repeated measurements agree with each other, which happens whenever the errors are consistent, and a consistent error is exactly what a systematic problem produces: a zero offset on a sensor, a miscalibrated scale, a ruler with a worn end. Every reading is shifted the same way, so the spread stays small while the mean sits away from the truth. Repeating the measurement more times cannot expose it. The remedy the AP Physics 1 CED suggests in its Science Practice 3 discussion is to design a second experiment to determine the same quantity and check the two for consistency.

Does taking more measurements make your results more accurate?

It makes them more precise, and it improves accuracy only when the errors are random. Random errors scatter on both sides of the true value, so averaging many of them lets them cancel, which is why a set of five widely scattered readings can still have a mean sitting on the accepted value. A systematic error sits on the same side every time, so averaging preserves it exactly. This matters for exam answers: offering repetition as a way to improve accuracy is not the same claim as offering it to reduce random uncertainty, and only the second is defensible in general.

What do significant figures tell you?

They report the precision of a value, and nothing about its accuracy. The digits you print are a claim about how well the quantity is known, so writing more of them than the measurement supports overstates your precision and writing fewer discards information you had. On the AP exam this is scored rather than stylistic: the CED defines the task verb Calculate as performing mathematical steps to arrive at a final answer including algebraic expressions, properly substituted numbers, and correct labeling of units and significant figures. A result quoted to five figures can still be systematically wrong by several percent, which is the whole point of keeping the two ideas separate.

What is the difference between percent error and experimental uncertainty?

Percent error compares your result with an accepted value, so it measures accuracy and it cannot be computed without a reference value from outside your experiment. Experimental uncertainty is the range within which your measured value plausibly lies, worked out from the resolution of your instruments and the spread of your repeats, so it describes precision and needs nothing external. A result can have a tiny uncertainty and a large percent error. Note that if you have two of your own measurements and no accepted value, comparing them gives a percent difference rather than a percent error. No percent-error formula is printed on the AP Physics 1 equation sheet.

How do you reduce experimental uncertainty in an AP physics lab?

Name a specific procedure rather than promising care. The published scoring guideline for the CED's sample Experimental Design and Analysis question credits two moves for one point: taking several measurements at the same value of the independent variable, or taking at least one measurement at several different values so that a graph can be plotted. The first attacks random scatter by averaging. The second lets you use a slope, which is immune to a constant offset in every reading and therefore attacks accuracy as well. Other specific moves are measuring a large multiple of a small quantity and dividing, such as timing ten oscillations of a pendulum rather than one, and designing a second experiment by a different method to cross-check the first.