Practice Signal vs Noise in Math

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

Quick Recap

Distinguishing meaningful patterns (signal) from random variation (noise) in data.

Is this pattern real or just coincidence? The fundamental question of data analysis.

Example 1

easy
A teacher tracks class average scores over 6 months: \{65, 67, 64, 68, 82, 85\}. Identify the noise (random month-to-month variation) and the signal (meaningful trend) in this data.

Example 2

medium
A polling company surveys 100 people monthly. In January, 48% support Policy X. In February, 51%. Explain whether this 3% change is signal or noise, using standard error.

Example 3

easy
You flip a coin 10 times and get 6 heads. Is this signal (the coin is biased) or noise (random variation)? Calculate the expected range of heads for a fair coin.

Example 4

hard
A radar system detects an object with signal strength 12 units. Background noise has mean 5 and SD 3. Calculate how many SDs the signal is above noise and determine if the object is detectable.
← Back to Signal vs Noise Worked Examples