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Accuracy vs Precision Targets

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About This MicroSim

People often use accurate and precise as if they meant the same thing. For clocks they do not.

  • An accurate clock shows the right time on average.
  • A precise clock gives very consistent readings, even if every reading is off by the same amount.

This MicroSim turns clock error into a dartboard. The red bullseye is the true time, and each ring is one more second of error. Every yellow dot is one reading of the clock. The purple X marks the average of the twenty readings.

Two kinds of error move the dots:

  • Bias is error that is the same every time, like a clock that always runs 3 seconds fast. It slides the whole cloud of dots away from the bullseye.
  • Spread is random error that changes from reading to reading. It scatters the dots.

The label in the panel classifies the readings. A set counts as accurate when the average lands within 1 second of the true time, and as precise when the readings have a standard deviation under 1 second.

How to Use

  1. Look at the opening target. It already shows twenty readings with a small bias and a small spread.
  2. Drag Bias (consistently off) to the right. The whole cloud moves away from the bullseye but stays tight. Watch the label change to "Precise but not accurate."
  3. Set bias back to 0 and drag Spread (random error) to the right. The cloud stays centered but spreads out: "Accurate on average but not precise."
  4. Press Take 20 readings to drop a fresh set of random readings with the same settings. Notice that the average and spread change a little each time.

Iframe Embed Code

You can add this MicroSim to any web page by adding this to your HTML:

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<iframe src="https://dmccreary.github.io/clocks-and-watches/sims/accuracy-vs-precision/main.html"
        height="537px"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Learning Objective

Students will differentiate accuracy from precision using a clock-error analogy (Bloom: Understanding, Analyzing).

Grade Level

9-12 (Clocks and Watches with AI)

Duration

10-15 minutes

Prerequisites

  • Clock drift and parts per million (ppm) from Chapter 13
  • The idea of an average

Activities

  1. Predict (3 min): Before touching the sliders, ask students which slider will move the purple X and which one will spread the dots. Record the predictions.
  2. Explore (5 min): Students find settings that produce each of the four labels and sketch each target in their notebooks.
  3. Connect to clocks (5 min): Match each label to a real clock. A DS3231 that is 2 seconds fast after a month is precise but not accurate. A clock read by hand from a blurry photo might be accurate on average but not precise.
  4. Discuss (2 min): Which kind of error can you fix with one correction? (Bias: subtract the known offset. Spread cannot be removed with a single correction.)

Assessment

  • Give students a target picture and have them name the result and say which slider caused it.
  • Ask: "A clock is always exactly 5 seconds fast. Is it accurate? Is it precise?"
  • Ask students to explain why taking more readings helps you find the bias but does not reduce the spread.

References

  1. Accuracy and precision - Wikipedia article with the classic target diagrams.
  2. DS3231 Datasheet - Analog Devices; lists the ±2 ppm accuracy of the DS3231.
  3. Normal distribution - Wikipedia; the random readings use a normal (Gaussian) distribution.
  4. p5.js randomGaussian() reference - The function used to generate the readings.