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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?

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    $\begingroup$ 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? $\endgroup$ Mar 10, 2013 at 21:37
  • $\begingroup$ I meant accumulative. I was looking for the answer you gave me below, thanks! $\endgroup$ 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). $\endgroup$ Mar 11, 2013 at 9:08
  • $\begingroup$ I didn't get that they were relative frequencies, however seems that you're right about that! $\endgroup$ 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
    Mar 11, 2013 at 17:20

2 Answers 2

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ListLinePlot[{data[[All, 1]], Accumulate[#]/Total[#] &@data[[All, 2]]}\[Transpose]]

Mathematica graphics

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

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  • $\begingroup$ Also # ~Riffle~ Accumulate[#2] ~Partition~ 2 & @@ Transpose[data], though I would use data[[All, 2]] = Accumulate @ data[[All, 2]]; data :-) $\endgroup$
    – Mr.Wizard
    Mar 11, 2013 at 3:34
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    $\begingroup$ also, transdata = Transpose[{data[[All, 1]], Accumulate@data[[All, 2]]}] $\endgroup$
    – Iiss
    Mar 11, 2013 at 4:35
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    $\begingroup$ 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
    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
    Mar 11, 2013 at 17:17

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