Practice Noise in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Noise is random variation in data that is not explained by the underlying pattern or model — the unpredictable fluctuations around the true signal.

The static on a radio—it's there, but it's not the music you want to hear.

Example 1

easy
A student measures their heart rate five times: \{72, 68, 75, 71, 74\} bpm. Identify the signal (true heart rate estimate) and the noise (variability), and calculate each.

Example 2

medium
Stock prices show daily fluctuations. Stock A has daily changes: \{+2\%, -1\%, +3\%, -2\%, +1\%\}. Stock B changes: \{+0.1\%, -0.1\%, +0.1\%, 0\%, +0.1\%\}. Identify which has more noise and what that means for investors.

Example 3

easy
A thermometer in a stable environment reads: \{20.1, 19.9, 20.2, 20.0, 19.8\}°C. The true temperature is 20°C. Calculate the noise (variability) and explain how taking more measurements would help.

Example 4

hard
In a medical trial, the treatment shows an improvement of 3 points on a pain scale, but each patient's response varies with SD = 8. With n = 25 patients, calculate the signal-to-noise ratio (SNR = effect/SE) and determine if the signal can be detected.
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