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Head Scratcher.

  • I have a range of numbers 7150 - 9150 (2000 difference)
  • Between that range, I am incrementing by 100.
  • I am calculating the percentage increase at each of the incremental increases.

The total range percentage increase 9150-7150/7150 does not equal the sum of the incremental percentages. See Attached Image.

More perplexing. - I am taking each incremental % change and multiplying by 3. So 1% becomes 3%, etc. - The SUM of the new percentage is around 74% (see image) - Incrementally also I am taking that new percent and calculating the rise in a number starting at the value of 60. (see image) - The final total of that new number go from 60 to 124 with a percent rise of 107%.
- This is way off from 74%.

Somewhere my calculations are awry.

Thank you for any help in comprehending these phenomena. I tried to spell out exactly what my calculations are in the attached image.enter image description here

Range   Percent Change  Original Percent * 3    Percent Applied To Value    
7150                                                  60    
7250    1.398601399%    4.19580420%                   62.51748252   
7350    1.379310345%    4.13793103%                   65.10441283   
7450    1.360544218%    4.08163265%                   67.76173580   
7550    1.342281879%    4.02684564%                   70.49039630   
7650    1.324503311%    3.97350993%                   73.29133920   
7750    1.307189542%    3.92156863%                   76.16550937   
7850    1.290322581%    3.87096774%                   79.11385167   
7950    1.273885350%    3.82165605%                   82.13731096   
8050    1.257861635%    3.77358491%                   85.23683213   
8150    1.242236025%    3.72670807%                   88.41336004   
8250    1.226993865%    3.68098160%                   91.66783955   
8350    1.212121212%    3.63636364%                   95.00121553   
8450    1.197604790%    3.59281437%                   98.41443286   
8550    1.183431953%    3.55029586%                  101.90843639   
8650    1.169590643%    3.50877193%                  105.48417100   
8750    1.156069364%    3.46820809%                  109.14258156   
8850    1.142857143%    3.42857143%                  112.88461292   
8950    1.129943503%    3.38983051%                  116.71120997   
9050    1.117318436%    3.35195531%                  120.62331757   
9150    1.104972376%    3.31491713%                  124.62188058   

28%           24.82%         74.45%                       107.70%   

(9150-7150)/7150=28%    SUM(J4:J24)=24.82%  SUM(K4:K24)=74.45%  124-60/60=107%  


    7250-7150/7150=1.39%    0.013986014     
    1.39%*3=4.19%   0.041958042     

    124-60/60=107%  1.077031343     

    28% * 3 <> 107% Calculations Way Off        
    24.8% * 3 <> 107%   Calculations Way Off
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1 Answer 1

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You can't add up relative changes in this way and expect the sum to be meaningful.

The reason is that the first change is relative to the first value, but the second change is relative to the second value, and so on. Even if there were only three numbers, that sum is meaningless. In other words, using the example with three numbers $$a<b<c$$ note that $$\frac{b-a}{a} + \frac{c-b}{b}\neq\frac{c-a}{a}$$

I'm sure the other issues arise from this.

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  • $\begingroup$ Thank you... Corrected my calculation. Now all increments are relative to the initial value. Works out well. a<b<c<d etc. b-a/a < c-a/a < d-a/a etc. Can now calculate forecasted % increase in value in a range easily. $\endgroup$
    – Stephen Gunn
    Commented Jun 11, 2018 at 18:14

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