There is this simple looking basic statistics question that asks to estimate its mean and standard deviation. I have some doubts and just want to make sure whether my working is correct.

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For part (i) Is it ok if I say the estimated mean is 41? I think this one is pretty straightforward.

For part (ii) it is very tempting to say the s.d. is 2, but between the 1st quartile and 3rd quartile we have 50% of the data, while for a normal distribution about 2/3 (not 50%) of the data lie between 1 s.d from the mean. Thats the only clue that I can think of. Is there any other way to estimate the s.d.?

Helps are greatly appreciated. Many thanks!


It's not clear to me why you say the mean is 41 and the standard deviation is 2. Because the box-and-whisker plot is not skewed it follows that your dataset is quite symmetric. This means the mean is close to the average of 39 and 63, which is 51.

As for the standard deviation, you can find for example here: http://en.wikipedia.org/wiki/Box_plot#mediaviewer/File:Boxplot_vs_PDF.svg that approximately 50% from your data lies between 0.6745 standard deviations from the mean. So I would say a good estimate of your standard deviation is $\frac{12}{0.6745} \approx 17.79$.


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