Let's assume there's a magical ball that bounces once every .5 seconds, and that there was a specific machine designed to calculate the rate of the ball's bounce (with error). After performing numerous readings of the ball's bounce using this machine, you have a collection of values describing the rate at which the ball bounces for this particular ball.(adsbygoogle = window.adsbygoogle || []).push({});

Now, say you have another magical ball that bounces once every .25 seconds, and used the same machine from before to read the rate at which this other ball bounces. After getting some data, you now have data on the bounce-per-.5-second ball and the bounce-per-.25-second ball.

Question: How would one be able to relate the accuracy and precision of this machine between the readings of the two balls?

Question from different perspective: Could you relate the standard deviation from readings from the first ball to readings from the second?

Question from another perspective: Would it be possible, after collecting readings from the first ball and the second ball, to estimate the readings present in a third magic ball which bounced at a different rate?

Question from yet another perspective: How would you analyze the machine's precision off a collection of balls with different bounce frequencies?

Any feedback would be greatly appreciated. Preferably, if this type of statistical analysis exists, I'd like to know the name. I'm having immense trouble finding this type of analysis using google.

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# Calculating variance of a single statistic from different collections of data

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