Measurement theory, not to be confused with (measure-theory), is the study of functions that preserve certain desirable properties. Its theoretical basis is popular in psychology, and it is related to statistical analysis of data, especially in deciding how data represents reality.

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Why is uncertainty in mean less

Any measurement, say length of any object, will have some errors. The random errors that are present in the measurement can be reduced if we take mean of a large number of samples. This is because the ...
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Calculate best estimate of multiple mesurements with known but varying variance

When multiple experiments measure the same physical quantity and give a set of answers $s={s_1,s_2,...,s_n}$ for $n$ measurement and give an error with different variances $v={v_1,v_2,...,v_n}$. How ...
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26 views

surface area of a prism with some missing lengths

Question: A prism has an equilateral triangular base with a perimeter of $12c$m. If the length of the prism is $24cm$, determine the total surface area of the prism. hint: What is the area of 1 ...
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36 views

Combining ±% with ±dB in measurement uncertainty

Firstly apologies if this is not the correct place to post this but wasn't sure which site would be good to ask regarding about measurement uncertainty calculation. I am trying to calculate the ...
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19 views

How do I state a reduction in cost?

I have developed an algorithm and am having a hard time stating its benefit versus a baseline. Suppose that the baseline cost of solving the problem is 1000 seconds. Now suppose that my algorithm ...
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1answer
160 views

Cantor-Lebesgue function and an increasing function are equal almost everywhere

Denote by $\varphi$ the cantor-lebesgue function and suppose $f$ is a certain increasing function defined on [0,1] and such that $f(x)=\varphi (x)$ for all $x\in[0,1]-C$ where $C$ is the cantor set. ...
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How can I tell whether my machine rounds or truncates?

I have an electronic weighing-machine, which I believe to be internally very accurate. It will weigh up to $100$ kg, but not activate below $10$ kg. The digital display reports to one decimal place. ...
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1answer
56 views

Uncertainty in measurements: if $x$ has uncertainty $\pm\epsilon$, what is the uncertainty in $\sin x$?

I have two questions regarding uncertainties in measurements. First, if I have some measured value for $x$ with an uncertainty $\pm e$, what would be the uncertainty in $\sin x$, $\pm\sin e$? ...
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503 views

Minimize combined variance of multiple measurements with known (but varying) variance

I have multiple measurements for the same property but with different but known uncertainty (variance). And I would like to combine that measurements in a way that I get as close to the real value as ...
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196 views

Finite additivity, atomlessness and countable additivity

So, I'm trying to get my head around when you can have finitely but not countably additive probabilities. The standard example of a finitely additive but not countably additive space is the ...