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?

#HelpMe!

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Comments

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

Namrata Haribal - 7 years, 11 months ago

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 - 7 years, 10 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" ?

Namrata Haribal - 7 years, 10 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 $s=\displaystyle \sum \frac{f_0(x_i)-f(x_i)}{n}$

Bob Krueger - 7 years, 10 months ago

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

Namrata Haribal - 7 years, 10 months ago

@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 - 7 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$