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If we can say that we're able to determine the weather at 10ms intervals, and if we observe that over a whole second (1000 samples) that it's raining at every sample, what is the accuracy rate within which we've calculated the weather for the second? I'm sure this sounds like homework to some, but it's not. I was reading a statement about sampling rates that claimed a sample every 10ms, and that the result was within 10% accuracy. I am not sure how they came up with this guarantee.

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That depends whether you calculated that it would be raining or not. The accuracy is 100% if yes, 0% if no. Flip response aside, it is hard to claim an accuracy rate for a single digital event. 10% accuracy should either refer to an analog prediction, in which case you should be within 10% of the measured value, or a many event digital prediction, in which case the observed rate should be within 10% of your prediction. But in the popular press, "10% accuracy" has no numeric content, it just means "pretty good, but not perfect".

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