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
5 years, 11 months ago

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3 votes

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I would really like your opinions so please do look at this post and reply.. Please!

Namrata Haribal - 5 years, 11 months 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 - 5 years, 11 months ago

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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 - 5 years, 11 months ago

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Let's have the true curve be f(x)f(x). Call the estimation of the curve f0(x)f_0(x). Sample several points (xi,f0(xi))(x_i,f_0(x_i)) from the estimation of the curve. We also know the points (xi,f(xi))(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: f0(xi)f(xi)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=f0(xi)f(xi)ns=\displaystyle \sum \frac{f_0(x_i)-f(x_i)}{n}

Bob Krueger - 5 years, 11 months ago

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@Bob Krueger You're awesome! Thanks a LOT.

Namrata Haribal - 5 years, 11 months 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 n1n-1 instead of nn.

Bob Krueger - 5 years, 11 months ago

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