## Re: [xsl] Re: summing up incrementally

 Subject: Re: [xsl] Re: summing up incrementally From: Paul Tremblay Date: Fri, 19 Dec 2003 04:29:53 -0500
```On Fri, Dec 19, 2003 at 07:12:36AM +0100, Dimitre Novatchev wrote:

>
> It is quite simple to see that the real comulative increase is the product
> of percentages of yearly increases, not their sum.
>
> E.g. two yearly increases of 50% each give 225% comulative increase. That is
> 1.5 x 1.5, or it may be calculated:
>
> In case the value is 100 at start, it would be 150 after year 1.
>
> An increase of 50% the second year is 50% of 150 -- that is 75.
>
> The value at the end of the second year is 150 + 75 = 225
>
> Therefore, the total increase is:  225/100 = 2.25 = 225%
>
> Your approach to calculating the total increase is wrong -- e.g. in the
> above case it woud give 100%, not 225%.
>

I see your reasoning. In fact, I cannot add up percentages. That gives
me a false value.

But I calculate percent increase by this formula:

% increase = (new -old)/old * 100

If someone says that their profits increased 100 percent, this usually
means it has doubled in value. Perhaps a mathmatician would correct me.
However, the modern high school math books teach percentage increase in
this way.

In your example, I would say that 225 has increased 125 percent from
100. I realize that technically this might be wrong (1.25 * 100 = 125).
On the other hand, if you are graphing the increase, you want to have
these figures:

Graph showing percentage increase for first three years
=======================================================
x	y
=	=
1	0
2	50
3	125

The slopes of the lines would be identical if you plotted raw data:

Graph showing raw profits for first three years
===============================================
x	y
=	=
1	100
2	150
3	225

Here is a partial representation of the real figures:

year	sales		% increase from last year
====	=====		=========================
1933:	250,516,527	---
1934:	270,684,797	108
1935:	268,740,483	100
1936:	290,386,935	108

The thesis--actually my girlfriend's thesis--tries to show that as
Woolworth chainstores modernized its buildings, its profits increased. I
want to make a line graph to illustrate this point.

These figures come from the publication itself. However, I just checked
them, using this formula:

% increase = (year - previousYear)/perviousYear * 100

Originally I had added the percentages to get a 16 percent increase by
year 1936 from 1933. If you work the math the right way ((new - old)/new
* 100), you come up with 16 percent. If you add the figures, you also
come up with 16 percent.

But of course, that is a mere coincidence. As you pointed out, you

To caculate the figures is to use 1933 as a base year.  Hence, this
formula:

% increase = (year - 250,516,527)/250,516,527 * 100

So for the 1934:

% = (270,684,797 - 250,516,527)/250,516,527 * 100 = 8

For 1935:

% = (268,740,483 - 250,516,527)/250,516,527 * 100 = 8

For 1936:

% = (290,386,935 - 250,516,527)/250,516,527 * 100 = 16

Or, if I do it your way:

1.08 * 1.00 * 1.08 = 1.16

Then subtract 100%, or 1, and I get the same answer. Okay, that makes
sense! If you start your graph at 0 rather than 100, you simply subract
100 from the result, as I did above.

Luckily, I entered the raw data in my XML as well as the percent
increase. I so simply did:

<xsl:vaiable name = "base-year" select = "/data/year/record[@month =
'December']/@target-year-to-date"/>

Then, when I want to find the percent increase, I can do:

<xsl:value-of select = "round((@target-year-to-date -
\$base-year)/\$base-year * 100)"/>

As I said in the last post, this math doesn't take inflation into
account. From 1934 to 1942, Woolworth increased around 70 percent.
Perhaps their sales did really increase this much; but I think inflation
would probably bring the number down.

Sorry this post is so long. I started off by thinking you didn't
understand my problem. Then I thought that you might be partially wrong.
And as I wrote it I realized you were completely correct.

Paul

--

PS 225 is 225% of 100

225 shows a 125% increase from 100

I think both these statements are correct?

************************
*Paul Tremblay         *
*phthenry@xxxxxxxxxxxxx*
************************

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```