Posted by: Gary Ernest Davis on: June 12, 2015

I wrote

Today I want toÂ show how this might beÂ easier Â to do in MathematicaÂ®.

First let’s define the function** zsf[data,k]** which calculates the proportion of data that lies within *k* standard deviations of the mean of the given data set:

**zsf[data_, k_] := Length[Cases[data, x_ /; Abs[x – mean[data]] <= k*StandardDeviation[data]]]/Length[data]**

The code “**Cases[data, x_ /; Abs[x – mean[data]] <= k*StandardDeviation[data]]”Â **keeps those instances, called x, of the data set that are withinÂ *k* standard deviations of the mean of the data.

As in R, we import the data as a text file from a URL:

**nosmokedata = Import[“http://www.blog.republicofmath.com/wp-content/uploads/2015/\06/nosmoke.txt”, “List”]**

The **“List”** option tells MathematicaÂ® to import the data string as a formatted (ordered) list, which in R would be seen as a vector.

We plot a histogram of the data:

**Histogram[nosmokedata]**

We calculate the fraction of data that lies within 1 standard deviation of the mean and express that both as a fraction and a floating point number:

**zsf[nosmokedata, 1]**

**N[%]**

270/371

0.727763

Then we plot *zsf[k]* as a function of *k* over the range 0 through 4, subdivided into 20 equal intervals, as well as present the resultsÂ in table form:

**T = Table[{N[k], N[zsf[nosmokedata, k]]}, {k, 0, 4, 4/20}];**

**TableForm[T, TableHeadings -> {None, {“k”, “zsf[k]”}}]**

**ListPlot[T, Joined -> True, Mesh -> All]**

Well, that’s it … the result could have been written very nicely in MathematicaÂ® and saved as a PDF, or as a CDF and placed as an interactive document on the Web.

R has similar capabilities, so you pays your money and takes yourÂ choices.

I just feel data analystsÂ should be aware there is a choice.

Now if Wolfram (Steve) could lower the price ofÂ MathematicaÂ® to $50Â …

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