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A student repeats experiments for the period of a pendulum with the same stopwatch . His measurements vary among one another by (1/10) seconds on the average . How many times must he repeat the experiment in order to determine the period to am accuracy of (1/100) seconds .

I am having no clue on how to proceed to this question .

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    The "accuracy" here is to be measured as the variance. Since the students' measurements are, from what I understand, independent experiments, the following property of variance is probably what you are looking for: https://en.wikipedia.org/wiki/Variance#Sum_of_uncorrelated_variables_.28Bienaym.C3.A9_formula.29 – 2017-02-16
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    Thanks for the response but could you just post the solution – 2017-02-16
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    Sorry, no time. Besides, I don't understand the phrase "measurements vary among one another by (1/10) seconds on the average". I have a feeling, this is supposed to give you some idea about the standard deviation $\sigma$. To connect the Wikipedia notation to your problem: $X_{i}$ is the $i$-th measurement of the period of the pendulum. $\sigma^2$ is the variance. – 2017-02-16
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    Your Questions will get a more enthusiastic reception here, if you give the source of the question, say what course is involved, and show your own thoughts about a possible solution. The reference to 1/10 is puzzling without knowing the context. – 2017-02-16
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    Are there any knowledge about the amount of measurements done to reach "accuracy" 1/10? – 2017-02-16
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    No further information is given about the question – 2017-02-16

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This may be a 'drill' problem from a statistics textbook. If $\sigma^2 = 1/10,$ and the data can be assumed to be normal, then a 95% confidence interval (CI) for the true mean period is $\bar X \pm 1.96\sigma/\sqrt{n}.$

The quantity $1.96\sigma/\sqrt{n}$ (half the width of the CI) is called the 'margin of error'. Maybe your problem wants the margin of error to be 1/100. If so, solve $1.96\sigma/\sqrt{n} = 1/100$ for $n.$

Disclaimer: I am only suggesting this because my guess above is a typical kind of problem in statistics courses when CIs are under discussion. However, typically the problems are much more clearly stated than this one, so there is no way for me to know if this is actually what is required.

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    Thanks for giving the answer but I am currently in high school and we don't have so advance statistics in our course so probably a easier solution is required and the answer is 100 turns . – 2017-02-17
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    With $\sigma = \sqrt{1/10},$ surely you can solve $1.96\sigma/\sqrt{n} = 1/100$ for $n$ to see if you get 100. Anyhow, good luck with whatever statistics you _are_ doing. // And if you ask future questions, please include something about your math level and the kind of course. That will improve chances of getting an answer you are ready to understand. – 2017-02-17