1
$\begingroup$

I have the following data:

data = {{0, 0}, {20, 1.4}, {25, 9.8}, {30, 32.2}, {35, 38.2}, {40, 15.6}, {45, 2.7}, {50, 0.1}};

where the second coordinates are frequencies measured as percent of total (adding, therefore, to $100$). I would like to produce a cumulative frequency plot. What would be the neatest way to do so?

Improve this question
$\endgroup$
6
  • 3
    $\begingroup$ I'm not sure whether you're correct describing your data as frequencies. I'm assuming you're using this phrase in a statistical context, meaning counts and not a physical context (in Hertz). Given you have cumulative frequency I suppose it's the former, but then how can you have non-integer values? $\endgroup$
    – Sjoerd C. de Vries
    Commented Mar 10, 2013 at 21:37
  • $\begingroup$ I meant accumulative. I was looking for the answer you gave me below, thanks! $\endgroup$
    – Frederik Brinck Jensen
    Commented Mar 11, 2013 at 7:10
  • $\begingroup$ I didn't say "cumulative" was wrong. I just made a remark about the values not being integer. I now assume they are relative frequencies and that therefore there's no reason for the term 'Total' in my answer (it does no harm either). $\endgroup$
    – Sjoerd C. de Vries
    Commented Mar 11, 2013 at 9:08
  • $\begingroup$ I didn't get that they were relative frequencies, however seems that you're right about that! $\endgroup$
    – Frederik Brinck Jensen
    Commented Mar 11, 2013 at 12:50
  • $\begingroup$ There still remain questions of the meaning and interpretation of these data, Frederik. E.g., does the appearance of {{0,0}, {20,1.4}, ...} mean that $1.4$% of the frequency lies within the interval $[0,20]$ or that $1.4$% lies *exactly* at $20$? Should the plot reflect the data accurately or--as suggested by the accepted answer--attempt to interpolate between the bin cutpoints? Evidently the interpolation must be monotonic, but should it necessarily be linear (as in the accepted answer)? $\endgroup$
    – whuber
    Commented Mar 11, 2013 at 17:20

2 Answers 2

Reset to default
10
$\begingroup$ 
ListLinePlot[{data[[All, 1]], Accumulate[#]/Total[#] &@data[[All, 2]]}\[Transpose]]

Mathematica graphics

Improve this answer
$\endgroup$
3
  • $\begingroup$ you probably meant Accumulate...data[[All,2]]? $\endgroup$
    – kglr
    Commented Mar 11, 2013 at 3:56
  • $\begingroup$ @kguler yeah, will correct figure when I'm near mma. Thanks. $\endgroup$
    – Sjoerd C. de Vries
    Commented Mar 11, 2013 at 6:35
  • 1
    $\begingroup$ Terse style (in the FrontEnd): ListLinePlot[{#, Accumulate@#/Tr@# &@#2}\[Transpose]] & @@ (data\[Transpose]) $\endgroup$
    – Mr.Wizard
    Commented Mar 11, 2013 at 8:08
2
$\begingroup$

You can transform the data as follows, and then plot transdata,

transdata = Partition[Riffle[data[[All, 1]], Accumulate@data[[All, 2]]], 2]

Surely this is a neat way, but it remains to be seen if its the neatest.

Improve this answer
$\endgroup$
4
  • $\begingroup$ Also # ~Riffle~ Accumulate[#2] ~Partition~ 2 & @@ Transpose[data], though I would use data[[All, 2]] = Accumulate @ data[[All, 2]]; data :-) $\endgroup$
    – Mr.Wizard
    Commented Mar 11, 2013 at 3:34
  • 2
    $\begingroup$ also, transdata = Transpose[{data[[All, 1]], Accumulate@data[[All, 2]]}] $\endgroup$
    – Iiss
    Commented Mar 11, 2013 at 4:35
  • 1
    $\begingroup$ Yes. This one looks good in the FrontEnd: {#, Accumulate@#2}\[Transpose] & @@ (data\[Transpose]) (By the way the only reason I haven't voted for this answer is that I honestly don't understand the question.) $\endgroup$
    – Mr.Wizard
    Commented Mar 11, 2013 at 4:59
  • $\begingroup$ @Mr.Wizard I have performed a somewhat aggressive edit of the question to reflect an interpretation suggested by the accepted answer. $\endgroup$
    – whuber
    Commented Mar 11, 2013 at 17:17

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.