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Calculation of Standard Deviation of coordinates?

Hello, I am currently in high school and we are learning about Standard Deviation. My teacher says that the applications of SD can be found in calculating the marks/population etc. But what I'm wondering is: can we calculate the SD of co-ordinates. For example, the cosine curve has a particular shape to it. But if a child draws it freehand, then it will not be as perfect as the cosine curve plotted by a calculator. So the curve drawn by the child deviates from the normal curve (and hence his curve has different co-ordinates.)

Now can we calculate the standard deviation for such a problem? What are your opinions?

Note by Namrata Haribal
4 years, 1 month ago

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Yes, you should be able to. Take several y-values of the child's curve and subtract them from the normal curve. From there you can average these and get the "standard deviation." It's basically like a normal standard deviation, except that the mean is not fixed, but it is the normal curve at the different sampled y-values. Bob Krueger · 4 years ago

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@Bob Krueger hey, thanks so much!! If its possible, can you give a more detailed explanation, please? what do you mean by "subtract them from the normal curve" ? Namrata Haribal · 4 years ago

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@Namrata Haribal Let's have the true curve be \(f(x)\). Call the estimation of the curve \(f_0(x)\). Sample several points \((x_i,f_0(x_i))\) from the estimation of the curve. We also know the points \((x_i,f(x_i))\) from the true curve. You can find the deviation of each of these points on the estimated curve from the true curve by subtracting: \(f_0(x_i)-f(x_i)\). Averaging these up will give you an approximate standard deviation. Of course, sampling more points will give you a better approximation. Thus \(s=\displaystyle \sum \frac{f_0(x_i)-f(x_i)}{n}\) Bob Krueger · 4 years ago

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@Bob Krueger You're awesome! Thanks a LOT. Namrata Haribal · 4 years ago

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@Namrata Haribal Thanks! :) This is just my guesswork though. This is the same general idea as finding the standard deviation from the best fit line in a linear regression situation. Also, because standard deviation is weird, you might want to try using \(n-1\) instead of \(n\). Bob Krueger · 4 years ago

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I would really like your opinions so please do look at this post and reply.. Please! Namrata Haribal · 4 years, 1 month ago

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