Noise Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

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

Solution

  1. 1
    Signal = best estimate of true heart rate = mean: xห‰=72+68+75+71+745=3605=72\bar{x} = \frac{72+68+75+71+74}{5} = \frac{360}{5} = 72 bpm
  2. 2
    Noise = variability around the mean: range = 75โˆ’68=775 - 68 = 7 bpm
  3. 3
    Standard deviation (noise measure): deviations are 0,โˆ’4,3,โˆ’1,20,-4,3,-1,2; ฯƒ2=0+16+9+1+45=6\sigma^2 = \frac{0+16+9+1+4}{5} = 6; ฯƒโ‰ˆ2.45\sigma \approx 2.45 bpm
  4. 4
    Interpretation: true heart rate is approximately 72 bpm, with typical fluctuation of about ยฑ2.45 bpm

Answer

Signal: 72 bpm. Noise: SD โ‰ˆ 2.45 bpm.
In any measurement, the signal is the underlying truth we seek to estimate, and noise is the random variation obscuring it. The mean estimates the signal; the standard deviation quantifies the noise. More measurements average out noise.

About Noise

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

Learn more about Noise โ†’

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