What is a Frequency Chart, how to generate?

[ptc-4310378]

Moderator: Please delete if this type inquiry is not appropriate. Just trying to tap into the vast knowledge base here......

Have an assignement coming up where we will have to classify a set of data via a frequency chart.

I intend to implement in Mathcad, but have never heard about this frequency scale on the chart. The Professor gave no references we could look up on the origin of the chart. He said he would give us instructions in Excel at a later date on how to build such a chart. Am curious if anybody here would be familiar with such a frequency plot and implementation in Mathcad?

From what I could see in class, the frequency scale on the absicissa starts at .01, with 50 in the middle of the axis and ends at 99.99. I'd say on this scale 1 would be about a third of the way to 50 and 20 at 2/3 of the way, then symetry on the other side of 50 with 70 at 1/3rd of the way to 99.99 and 99 at 2/3rd of the way.

Anybody familiar with this "frequency" scale and its origin/background and how to generate a graph based on this scale from a set of data pairs?

Thank you.

[MichaelH]

Many types of data distributions fit a "Gaussian" (also called "Normal") distribution, which sounds like what you are looking for. If the outcome of an event has only two possibilities (such as heads or tails from a coin toss), it is called the "Binomial" distribution.

You can use the "Histogram" function in Mathcad to "bin" the data and see how it fits.

Any introductory book on statistics should cover this in sufficient detail.

[ptc-4310378]

I found freeware that will generate the plot I need against this lognormal scale.

http://www.zonums.com/lnpp.html

Just not sure about the theory behind it for duplicating in Mathcad. Was hoping somebody may have done it with Mathcad before.

Otherwise, looks like this freeware will do.

[MichaelH · Accepted solution]

Mathcad does not specifically have a graph like this as far as I know, but you can make one that has similar characteristics by using the Weibull distribution functions. The x-axis will be in standard deviations from the mean, but you can easily convert this to percentiles using these functions.

There is a sample worksheet (a.k.a. "Quicksheet") showing how normal distribution functions are related to percentiles under the "Normal Distribution" topic. It should not be too much effort to convert this into a Weibull plot.

[ptc-4310378]

Thanks for the guidance on that. This is all new to me. Not sure why the Professor referred to this as a "Frequency" chart in class. But the HomeWork assignement only gives a "recipe" like method to derive a coefficient from a log normal plot that can be generated in Excel, without much explanation of what is at stake here.

From papers on this log normal derived Dykstra-Parson coefficient we are after, it looks like it can actually be derived directly from the cumulative log normal function, without going through the extra step of plotting. It will probably be clearer once I find the original paper on that.

But due to the short time we have for the assignement, I may have to reluctantly stick with the blind Excel cookie cutter recipe and try to understand it via Mathcad during my leisure time. But it will be easier once I know from the Excel excercise what results need to be matched (I usually like to do the reverse, validate my classmates Excel results with the Mathcad results....)

Thanks.

[MichaelH]

The example graph you linked to had the word "Weibull" on it, which I thought referred to the distribution being a Weibull one.

But it may be a "normal" distribution based on other material on the internet.

I agree with you on the cookie cutter approach for now. Hold you nose and use Excel.

[ptc-4310378]

Well...the work has really been chewed down for us in the Excel assignment sheet. No idea what it all means, but all we have to do is plug our data in the Excel Sheet and the plot is generated. So I'll go this road and try to undersand later...

Looking at the formula in the sheet, I can see NORMINV being used which is most likely the equivalent to Mathcad qnorm you had mentioned?

Also, there is a constant 3.71947 being used. Is this a constant well known by those skilled in the art?

[MichaelH]

In Excel, NORMINV(probability, mean, std_dev) returns the inverse of the normal cumulative distribution for the specified mean and standard deviation.

The equivalent in MC15 is qnorm(). I also see that MC15 has "log normal distribution" functions, which might be useful for your task. I've never used them.

3.719 is the (approximate) number of standard deviations to the right of the mean where the 99.99th percentile begins for a normal distribution.

BTW - One of my pet peeves (among many) is professors or bosses who have just enough skill or facility in Excel to make a complicated "template" file that they absolutely insist you use, not because it's so good, which it is not, but because they think it somehow shows the world how clever or computer savvy they are. I've seen huge multi-column spreadsheets of data that Mathcad could have chewed up and spit out in a few lines. Ugh!

[ptc-4310378]

There is some savvy behind this Excel Chart. Never saw anything quite like that before. The Professor had even hid away the worksheet (adequately named "Charts Lines") where the scale is referenced from, to make it look like magic! After "unhiding" the sheet, it becomes easier to understand how it is done.

Each vertical grid line on the graph (23 of them) is actually a "series", a straight vertical line defined between 0 and a number large enough so you never see the end of it. The coordinate of the line fits the percentile distribution (to cover his tracks, he has erased the formula used to get to this number......only "values" left in the cells....! So I have to reverse engineer this one). Then he cleverly uses the label for each series (vertical lines) as a marker for the scale along this abscissa. Quite amazing (to me at least).

One of the reasons I prefer working it out in Mathcad, is that if I ever have a use for it later in the real world, I can catch up with the logic behind the calcs pretty fast. Not so with Excel sheets. Proof is that I had fellow students asking for a PDF of my HW Mathcad files before, when I knew they were already being helped by others via Excel sheets, but they prefer the Mathcad file that they find easier to decipher.

I've attached the Excel file in case you'd like to have a look at the chart ("Chart" tabs).

For the purpose of this HW, I am done: Only two points to read on the graph to determine a coefficient and five more to complete the HW task. But I am pretty sure it would be possible to calculate the coefficient directly from the data in Mathcad, without ever plotting the data. Although the plot is nice to look at to confirm the linear trend (lognormal distribution), which is the basis of the analysis.

Thanks for your insights.

[MichaelH]

There is some savvy behind this Excel Chart. Never saw anything quite like that before. The Professor had even hid away the worksheet (adequately named "Charts Lines") where the scale is referenced from, to make it look like magic! After "unhiding" the sheet, it becomes easier to understand how it is done.

I'm sometimes amazed at the spreadsheet gymanastics that people go through in Excel.

It becomes incredibly dense with calculations referencing cells that reference other cells that reference other cells that...and so on. In some cases, I'm not sure if the answer is right or not, but by that point I have a headache and don't care anymore.

At least with Mathcad there is a good chance of figuring out what another person has done.

[StuartBruff]

MichaelH wrote:

I'm sometimes amazed at the spreadsheet gymanastics that people go through in Excel.

It becomes incredibly dense with calculations referencing cells that reference other cells that reference other cells that...and so on. In some cases, I'm not sure if the answer is right or not, but by that point I have a headache and don't care anymore.

At least with Mathcad there is a good chance of figuring out what another person has done.

Tell me about it, already. I checked out one Excel worksheet that had been used to determine the choice of numerical integrator for a 6-dof simulation program. The big clue to the fact that there might have been errors in the worksheet was that the 4th order Runge-Kutta integrator performed worse than the simple Euler. Tracking the error down wasn't easy because of the cell referencing scheme used.

I don't even trust my own Excel worksheets, let alone anybody else's!

Stuart

[ptc-4310378]

Thanks to your pointers, I was able to handle the HW in Mathcad and gain some understanding on what was being done. As you said, not much to it.....once you know how to do it! And more fun than blindly plugging numbers in the ready-made Excel assignement sheet.

Thanks for the help.