# 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, 4 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.

- 5 years, 4 months ago

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" ?

- 5 years, 4 months ago

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 $$s=\displaystyle \sum \frac{f_0(x_i)-f(x_i)}{n}$$

- 5 years, 4 months ago

You're awesome! Thanks a LOT.

- 5 years, 4 months ago

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 $$n$$.

- 5 years, 4 months ago