The water temperature is 19 C, which is true value. I have measured the temperature of the water and I received such results: 18.7, 18.8, 19.1, 18.8. Can I calculate variance here around true value (19), but not around mean?
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1$\begingroup$ Sure, you can carry out that calculation -- but what is your objective in doing so? $\endgroup$– whuber ♦Commented Jun 20 at 15:19
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$\begingroup$ My aim is to find measurement error R (Kalman filter) which I can use in the second experiment. I assume that variance found in this way(by using not mean but 19) is a measurement error, am I right? $\endgroup$– Max HeronCommented Jun 20 at 16:11
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$\begingroup$ This is usually known as the mean square error. The "error" refers to the difference between a reading and the true value; in your case, the differences $18.7-19,$ $18.8-19,$ etc. Their squares are $(18.7-19)^2,$ etc. "Mean" is used in the usual sense of the arithmetic mean. $\endgroup$– whuber ♦Commented Jun 20 at 16:45
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$\begingroup$ Thanks. And the average between ((18.7−19)^2+(18.8−19)^2+(19.1−19)^2+(18.8−19)^2)/4=0.045 is my Measurement error R? $\endgroup$– Max HeronCommented Jun 20 at 17:54
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$\begingroup$ That would be your mean square error. People usually report its square root, the root mean square error (RMSE). $\endgroup$– whuber ♦Commented Jun 20 at 19:48
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yes you can, if you do you may use the whole sample size as the denominator (n instead of n-1, as you aren't using any degree of freedom for estimating the mean), however, you may get a bad result if your tool is biased in measuring temperature.
if you measure the mean square error around the true temperature value, that will be the sum of the variance and the square of the bias, if the bias is zero, you will get the variance.
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$\begingroup$ My aim is to find measurement error R (Kalman filter) which I can use in the second experiment. I assume that variance found in this way(by using not mean but 19) is a measurement error, am I right? $\endgroup$ Commented Jun 20 at 16:09
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$\begingroup$ it is a measurement error, yes, it's the mean square error, as whuber told you already, the same mean square error I mentioned in my answer. the equation between MSE and the sum of the variance and the sqaure of the bias is called bias-variance tradeoff. anyway, my answer refers to the simple temperature example you gave us, you should make a new question about your problem with Kalman filter application, providing all details in the question rather than disclosing them in the comments. $\endgroup$– carloCommented Jun 21 at 7:52