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My question is, if after repeated measurements the $\delta l$ value i.e. $$\frac{1}{n}\sum^{n} {(x_i-\bar x)^2}$$ comes to be less than Least Count of the instrument used.

$$\delta l \leq L.C.$$ Then would the my measurement be written as $$ l \pm \delta l$$ or $$ l \pm \text{least count value of instrument}$$ ?

Where $l$ is the average of all measurements (without error).

Thanks.

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Here's an example to help you think about it yourself: suppose you're measuring a stick with a metre scale, and the closest value consistently comes out to be 28.3 cm over 100 measurements. Which do you think makes more sense: that the length of the stick is exactly 28.3 cm (all the way down to the atomic scale), or that any variation from 28.3 cm is just smaller than the least count of your instrument?

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  • $\begingroup$ I get it, the variation that I thus shall obtain would be Mean absolute val. (The value which is not depicted my the instrument because of its limitation but because of repeated measurements I get it through average). Thanks. $\endgroup$
    – mnuizhre
    Commented Nov 27, 2020 at 9:02

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