!@#%#$ Math

[bcholmes]

Okay, I can't figure out the math on this problem. Can anyone help me?

I have a bunch'a numbers. Response times from a web server. I round off these response times into nice numbers. Closest 100 milliseconds or sumpthin. For every 100 millisecond interval, I count the number of occurences, giving me a pretty graph, like this.

Now I want to do standard deviation stuff. I calculate the standard deviation of the response times. Turns out, in my case, to be about 300 milliseconds. Big spread. Clustered in the [0s-0.5s] range.

Now, standard deviations are ideal for drawing the dreaded bell curves:

And I know that for each sigma, we're covering a larger percentage of the occurrences. In the following picture, for example:

the red area is supposed to cover something like 68% of the data, if the arrow marks out one sigma.

What I ultimately want to do is to render a graph with the standard deviation curve superimposed over the bar chart:

My question: how the hell do I calculate meaningful Y values for the standard deviation curve? I figure that the mid-point should be 50% of my total number of occurrences. How do I get the other points?

(Did I mention that I didn't do all that well in statistics? Or Fourier Analysis, but that's a whole 'nuther story).

Comments

What I remember from stats

[sara-wolfe.livejournal.com]

I *think* you already have a "curve that's slanted to the right". If I remember my terminology correctly (only been three months since I took stats, and already forgot!), but I think that's what it is. It is, as one of the people on here noted, a way to draw up frequencies.

Here's a useful site: http://www.robertniles.com/stats/

More: http://www.math.hmc.edu/~gu/math142/mellon/curves_and_surfaces/curves/bell.html

I'm not awake yet, so I might be confusing what you're asking for. Are you saying that the distribution you have is not normal, and you want to find a way to make it normal?

What you have does not look like a normal distribution since everything since you have a higher density on the right than to the left.

I have a whole department full of statisticians here, so let me know if you still need help.

Re: What I remember from stats

[bcholmes.livejournal.com]

Oooo, this formula looks promising:

But what's capital-E in the equation?

What I'm trying to do is show the normal distribution compared to the actual frequency, so that people can get an immediate visual sense of the fact that the data isn't normalized (for whatever reason). If the data is reasonably normalized, I'd expect the bars to line up neatly under the curve. Make sense?

Re: What I remember from stats

[the-fury.livejournal.com]

Natural base of logarithms...

2.718282

Re: What I remember from stats

[bcholmes.livejournal.com]

That's capital-E? I thought that was little-e.

Re: What I remember from stats

[the-fury.livejournal.com]

Heh. Yeah, it's supposed to be. Probably be a typo on their part.

http://www.ruf.rice.edu/~lane/hyperstat/A25726.html

Gives the same thing with a small e.