General Chemistry I (CHEM-UA), Lab 2 | Source: Data Analysis Lab Handout (Geggier, NYU)
Tags: accuracy, precision, systematic error, random error, bias, reproducibility, data quality, measurement error, lab technique
Difficulty: Introductory | Prerequisites: None. This is foundational material for all subsequent labs.
Every number you record in the lab carries two hidden questions: how close is it to the real value, and how close would it be if you measured again? This topic sits right at the start of the course because every calculation, graph, and conclusion you produce later depends on whether the data feeding it is any good. If you cannot tell whether a dodgy result comes from a broken instrument or from ordinary human wobble, you cannot fix it. The concepts here, accuracy, precision, systematic error, random error, reappear in every single lab report you will write.
Accuracy is how close a measurement lands to the true value; precision is how close repeated measurements land to each other. Systematic errors push every reading in one direction (hurting accuracy), while random errors scatter readings unpredictably (hurting precision). You fix systematic errors by finding and removing the cause; you manage random errors by repeating measurements and averaging.
Accuracy
How close a measurement is to the true (accepted) value. Accepted values come from skilled scientists using the best available instrumentation and are published in reference books.
In simple terms, accuracy answers the question: "Did I hit the bullseye?"
Precision
The measure of how close or reproducible a series of experimental measurements are to each other. A data set can be highly precise without being accurate.
Think of it as: "Are my arrows clustered together, regardless of where on the target they landed?"
Systematic error (determinate error)
An error caused by a faulty measuring device, a flawed method, or a consistent personal mistake. Systematic errors always shift data in the same direction (always too high or always too low).
In simple terms, this is a bias baked into your setup. Every reading is off by roughly the same amount and in the same direction.
Random error (indeterminate error)
An error that arises from operator skill and instrument precision. Small mechanical fluctuations or differences in human technique cause individual readings to scatter above and below the true value unpredictably.
Think of it as: the wobble you cannot fully control no matter how careful you are.
A data set can have high precision but low accuracy (tight cluster, wrong target).
High accuracy cannot be achieved without high precision. If your readings scatter widely, their average is unreliable.
The classic dartboard analogy:
High accuracy + high precision: tight cluster on the bullseye.
Low accuracy + high precision: tight cluster away from the bullseye (systematic error).
Low accuracy + low precision: scattered all over the board.
High accuracy + low precision: this combination is not reliably achievable.
Cause: a faulty instrument, a flawed procedure, or a repeated personal mistake.
Direction: always the same. Every measurement is shifted the same way (all too high, or all too low).
Effect: reduces accuracy. Precision may still look fine because readings are consistent with each other.
How to fix: identify the source and correct it. Repeating the experiment does not help if the same bias is present every time.
Examples from this lab:
Reading a buret consistently from the wrong angle (parallax).
Using a balance that was calibrated at a different temperature than the room.
Not drying a graduated cylinder before measuring volume, so residual water dilutes the sample every time.
Small particles passing through filter paper in a filtration experiment (consistent loss of solid).
Cause: operator skill variations and inherent instrument limitations.
Direction: unpredictable. Individual readings may be too high or too low.
Effect: reduces precision. The spread of data increases.
How to fix: repeat the measurement many times and calculate the average. The random fluctuations tend to cancel out.
Examples from this lab:
Reading the volume of liquid in a 100 mL graduated cylinder as 35.5, 35.6, or 35.7 mL depending on exactly where you position your eye.
Slight differences in how firmly you tap a container to settle its contents.
Minor mechanical fluctuations in a balance reading.
The key test is direction. If you can tell that every reading is shifted the same way relative to the accepted value, you likely have a systematic error. If readings scatter in both directions around the mean, that scatter is random error. In most real experiments both types are present at the same time.
"If my measurements are precise, they must be accurate." They are not the same thing. A miscalibrated balance can give you beautifully consistent readings that are all wrong by the same amount. Precision says nothing about whether you are hitting the true value.
"Repeating the experiment fixes all errors." Repeating and averaging reduces random error. It does nothing to fix systematic error, because the same bias is present in every trial.
"A single measurement can tell me whether I have systematic or random error." You need multiple measurements. A single reading gives you no information about precision, and without a known true value you cannot assess accuracy either.
"Random error means I made a mistake." Random error is always present, even with perfect technique. It is a feature of measurement itself, not evidence of carelessness.
⚠️ Worksheet I Question 1 asks you to classify specific lab scenarios as systematic (S) or random (R). The trick is to ask: does the error always push in one direction, or does it scatter?
⚠️ You will be expected to explain the difference between accuracy and precision in your own words, with examples.
⚠️ Knowing that high accuracy requires high precision (but not the reverse) is a classic exam point.
⚠️ Be ready to identify what type of error is present in a described experimental setup and suggest how to correct it.
True or False: A set of measurements can be precise but not accurate. (True)
True or False: Averaging many measurements eliminates systematic error. (False, it only reduces random error)
Fill in the blank: Systematic errors always affect data in the same __________. (direction)
True or False: High accuracy is possible without high precision. (False)
Fill in the blank: To reduce random error, scientists repeat an experiment many times and calculate the __________. (average/mean)
Q: A student uses a balance calibrated at 18 °C when the lab is at 28 °C. Is this a systematic or random error? Explain.
A: Systematic. The calibration offset is consistent across every measurement, pushing all readings in the same direction.
Q: Three students each measure the density of a metal three times. Group A gets 11.08, 11.03, 11.06 g/cm³. Group B gets 10.1, 10.3, 10.5 g/cm³. The accepted value is 10.4 g/cm³. Which group is more precise? Which is more accurate?
A: Group A is more precise (smaller spread). Group B is more accurate (their mean of 10.3 g/cm³ is closer to the accepted value of 10.4 g/cm³ than Group A's mean of 11.06 g/cm³).
Q: A student repeats a mass measurement and gets 0.5439 g, 0.5438 g, and 0.5440 g. What type of error causes the small differences between readings?
A: Random error. The slight variations in each direction are due to operator skill and instrument sensitivity.
Q: You rinse a graduated cylinder but do not dry it before measuring the volume of a liquid. How does this affect your result, and is it a systematic or random error?
A: Systematic error. The residual water consistently adds extra volume, so every reading is shifted higher than the true volume of the liquid being measured.
Q: Can you detect a systematic error by repeating measurements and looking at the spread? Why or why not?
A: No. The spread (precision) can look excellent even when every reading is biased. You need a known accepted value, or an independent method, to detect systematic error.
This material connects directly to significant figures (the next topic in this lab), because the number of significant figures you record reflects the precision of your instrument. It also sets the stage for standard deviation and percent error, which are the numerical tools you will use to quantify precision and accuracy, respectively. Every lab report you write this semester will require you to assess data quality using these concepts.
Related Terms / Search Tags
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