Firstly, we have an array of predetermined factors, ie. V-Z;
their attributes are 3, the first two (•xM) multiplied giving the 3rd.
f ... factors
• ... cap, the values in the data set may increase max
m ... fixed multiplier
p ... let's call it power
This is a separate, standalone array .. we'd access with eg. VLOOKUP
f • m pwr
V 1 9 9
W 2 8 16
X 3 7 21
Y 4 6 24
Z 5 5 25
—————————————————————————————————————————————
Then we have 6 columns, in which the actual data to be processed is in, & thereof derive the next-level result, based on the interaction of both samples introduced.
In addition, there are added two columns, for balance & profit.
Here's a short, 6-row data sample:
f • m bal profit
V 2 3 377 1
Y 2 3 156 7
Y 1 1 122 0
X 1 2 -27 2
Z 3 3 223 3
—————————————————————————————————————————————
Ultimately, starting at the end, we are comparing IF -27 inverted → so 27 is within the X's power range ie. 21 (as per the first sample) .. which is then fed into a bigger formula, beyond the scope of this post.
This can be done with VLOOKUP, all fine by now.
—————————————————————————————————————————————
To get to that .. for the working example, we are focusing coincidentally on row5, since that's the one with the first negative value in the 'balance' column, so ..
on factorX = which factor exactly is to us unknown &
balance -27 = which we have to locate amongst potentially dozens to hundreds of rows.
Why!?
Once we know that the factor is X, based on the * & multiplier pertaining to it, then we also know which 'power' (top array) to compare -27, as the identified first negative value in the balance column, to.
Is that clear?
I'd like to know the formula on how to achieve that, & (get to) move on with the broader-scope work.
—————————————————————————————————————————————
The main issue for me is not knowing how to identify the first negative or row -27 pertains to, then having that piece of information how to leverage it to get the X or identify the factor type, especially since its positioned left of the latter & to the best of my knowledge I cannot use negative column index number (so, latter even if possible is out of the question anyway).
To recap;
IF(21>27) = IF(-21<-27)
27 → LOCATE ROW with the first negative number (-27)
21 → IDENTIFY the FACTOR TYPE, same row as (-27)
→ VLOOKUP pwr, based on factor type identified (top array, 4th column right)
→ invert either 21 to a negative number or (-27) to the positive number
= TRUE/FALSE
Guessing your columns I'll say your first chart is in columns A to D, and the second in columns G to K
You could find the letter of that factor with something like this:
=INDEX(G:G,XMATCH(TRUE,INDEX(J:J<0)))
INDEX(J:J<0) converts that column to TRUE and FALSE depending on being negative or not and with XMATCH you find the first TRUE. You could then use that in VLOOKUP:
=VLOOKUP(INDEX(G:G,XMATCH(TRUE,INDEX(J:J<0))),A:D,4,0)
That would return the 21. You can use the first concept too to find the the -27 and with ABS have its "positive value"
=VLOOKUP(INDEX(G:G,XMATCH(TRUE,INDEX(J:J<0))),A:D,4,0) > INDEX(J:J,XMATCH(TRUE,INDEX(J:J<0)))
That should return true or false in the comparison
I'm trying to calculate a weighted median, but don't understand the difference between the following two methods. The answer I get from weighted.median() is different from (df, median(rep(value, count))), but I don't understand why. Are there many ways to get a weighted median? Is one more preferable over the other?
df = read.table(text="row count value
1 1. 25.
2 2. 26.
3 3. 30.
4 2. 32.
5 1. 39.", header=TRUE)
# weighted median
with(df, median(rep(value, count)))
# [1] 30
library(spatstat)
weighted.median(df$value, df$count)
# [1] 28
Note that with(df, median(rep(value, count))) only makes sense for weights which are positive integers (rep will accept float values for count but will coerce them to integers). This approach is thus not a full general approach to computing weighted medians. ?weighted.median shows that what the function tries to do is to compute a value m such that the total weight of the data below m is 50% of the total weight. In the case of your sample, there is no such m that works exactly. 28.5% of the total weight of the data is <= 26 and 61.9% is <= 30. In a case like this, by default ("type 2") it averages these 2 values to get the 28 that is returned. There are two other types. weighted.median(df$value,df$count,type = 1) returns 30. I am not completely sure if this type will always agree with your other approach.
I'm trying to make a formula that transforms a list decimal numbers to binary, then counts the number of appearances of ones at a certain position. I was trying to build an array formula that went something like this:
{=SUM(MID(DEC2BIN(A1:A10;10);9;1)}
This will return #VALUE. Is there a way to do this?
EDIT: examples added
Input (Binary Equivalent)
2 0000000010
3 0000000101
7 0000000111
7 0000000111
5 0000000101
9 0000001001
Outputs Result
(digit to sum
from the right)
1 5
2 3
3 3
4 1
This was another way e.g. for the second digit from the right
=SUMPRODUCT(--ISODD(A1:A10/2))
Divide by 2^(n-1) where n is digit numbered from the right: the ISODD function ignores any fraction that results from the division.
=SUM(0+MID(DEC2BIN(--A1:A10,10),9,1))
array-entered.
Regards
If you are trying to count have many of the second digits are set in a range of numbers you can do this:
={SUM((MOD(A1:A10,4)>=2)+0)}
To understand this, let's look at some example data
Here I have some decimal numbers with their binary equivalents. In column C I have just extracted the 2nd digit (i.e. your MID(A1,9,1)). Then in column D I just take the modulo by 4. You can see that when the remainder is greater than 2, the second digit is set.
MOD(A1,4) basically divides the number by 4 and gives us the remainder (the numerator of the remainder if it was represented as a fraction over 4). With binary numbers, division by a power of two is just a right shift. Division by 4 is a right shift by 2 and the numbers that 'fall off' are the remainder. In this case it's the first two digits. They can be
00 | 0
01 | 1
10 | 2
11 | 3
so we see that the second digit is set only when the remainder is greater than 2.
Note the +0 in the original formula is to cast the boolean result of = to an integer so we can use SUM i.e. SUM({TRUE,FALSE}) doesn't work but SUM({TRUE,FALSE}+0) computes to SUM({1,0}) which does work.
To make this generic, let's assume you want to do it for the $E$1th digit:
=SUM((MOD(A1:A12,2^$E$1)>=2^($E$1-1))+0)
With bit operations it's not necessary to treat the number as a string.
{=SUM(BITAND(A1:A10;2^(C1-1))/2^(C1-1))}
Assuming the position you are looking for is stored in C1.
I have an risk control assessment where some controls are key and hold greater weight than non key controls.
Key vaule (1-4)
Y 4
Y 3
N 2
N 2
I want the keys with a "Y" to be summed at a weight of 70% and the non-keys with an "N" to be summed at a weight of 30%.
If we add the column we get 11. However, I want the 7 (4+3) to be multiplied by 70% and the 4 (2+2) be multiplied by 30%.
There may be 4 rows or 40. There generally are only 1 or 2 key controls ("Y"), but, if there are 40 rows or controls, there may be up to 5 "Y"s.
Any thoughts?
A simple way to do what I think you want would be to create a third column that had formulas like this one: =IF(A1="Y",B1*0.7,B1*0.3). Then, you could use the SUM function to add up all of the results. See the cells with formulas below.
Key Value Weighted Value
Y 1 =IF(A2="Y",B2*0.7,B2*0.3)
N 2 =IF(A3="Y",B3*0.7,B3*0.3)
N 3 =IF(A4="Y",B4*0.7,B4*0.3)
Y 4 =IF(A5="Y",B5*0.7,B5*0.3)
=SUM(C2:C5)
Here would be the result...
Key Value Weighted Value
Y 1 0.7
N 2 0.6
N 3 0.9
Y 4 2.8
5
As you can seen from #TimWilliams' comment, there is some uncertainty about your requirement but if it is weighting factors then the following formula might suit:
=IF(A2="Y",C$1*SUM(B:B)*B2/SUMIF(A:A,"=Y",B:B)/SUM(B:B),(1-C$1)*SUM(B:B)*B2/SUMIF(A:A,"=n",B:B)/SUM(B:B))
copied down to suit and assuming a layout as shown:
I am trying to calculate percentage growth in excel with a positive and negative number.
This Year's value: 2434
Last Year's value: -2
formula I'm using is:
(This_Year - Last_Year) / Last_Year
=(2434 - -2) / -2
The problem is I get a negative result. Can an approximate growth number be calculated and if so how?
You could try shifting the number space upward so they both become positive.
To calculate a gain between any two positive or negative numbers, you're going to have to keep one foot in the magnitude-growth world and the other foot in the volume-growth world. You can lean to one side or the other depending on how you want the result gains to appear, and there are consequences to each choice.
Strategy
Create a shift equation that generates a positive number relative to the old and new numbers.
Add the custom shift to the old and new numbers to get new_shifted and old_shifted.
Take the (new_shifted - old_shifted) / old_shifted) calculation to get the gain.
For example:
old -> new
-50 -> 30 //Calculate a shift like (2*(50 + 30)) = 160
shifted_old -> shifted_new
110 -> 190
= (new-old)/old
= (190-110)/110 = 72.73%
How to choose a shift function
If your shift function shifts the numbers too far upward, like for example adding 10000 to each number, you always get a tiny growth/decline. But if the shift is just big enough to get both numbers into positive territory, you'll get wild swings in the growth/decline on edge cases. You'll need to dial in the shift function so it makes sense for your particular application. There is no totally correct solution to this problem, you must take the bitter with the sweet.
Add this to your excel to see how the numbers and gains move about:
shift function
old new abs_old abs_new 2*abs(old)+abs(new) shiftedold shiftednew gain
-50 30 50 30 160 110 190 72.73%
-50 40 50 40 180 130 220 69.23%
10 20 10 20 60 70 80 14.29%
10 30 10 30 80 90 110 22.22%
1 10 1 10 22 23 32 39.13%
1 20 1 20 42 43 62 44.19%
-10 10 10 10 40 30 50 66.67%
-10 20 10 20 60 50 80 60.00%
1 100 1 100 202 203 302 48.77%
1 1000 1 1000 2002 2003 3002 49.88%
The gain percentage is affected by the magnitude of the numbers. The numbers above are a bad example and result from a primitive shift function.
You have to ask yourself which critter has the most productive gain:
Evaluate the growth of critters A, B, C, and D:
A used to consume 0.01 units of energy and now consumes 10 units.
B used to consume 500 units and now consumes 700 units.
C used to consume -50 units (Producing units!) and now consumes 30 units.
D used to consume -0.01 units (Producing) and now consumes -30 units (producing).
In some ways arguments can be made that each critter is the biggest grower in their own way. Some people say B is best grower, others will say D is a bigger gain. You have to decide for yourself which is better.
The question becomes, can we map this intuitive feel of what we label as growth into a continuous function that tells us what humans tend to regard as "awesome growth" vs "mediocre growth".
Growth a mysterious thing
You then have to take into account that Critter B may have had a far more difficult time than critter D. Critter D may have far more prospects for it in the future than the others. It had an advantage! How do you measure the opportunity, difficulty, velocity and acceleration of growth? To be able to predict the future, you need to have an intuitive feel for what constitutes a "major home run" and a "lame advance in productivity".
The first and second derivatives of a function will give you the "velocity of growth" and "acceleration of growth". Learn about those in calculus, they are super important.
Which is growing more? A critter that is accelerating its growth minute by minute, or a critter that is decelerating its growth? What about high and low velocity and high/low rate of change? What about the notion of exhausting opportunities for growth. Cost benefit analysis and ability/inability to capitalize on opportunity. What about adversarial systems (where your success comes from another person's failure) and zero sum games?
There is exponential growth, liner growth. And unsustainable growth. Cost benefit analysis and fitting a curve to the data. The world is far queerer than we can suppose. Plotting a perfect line to the data does not tell you which data point comes next because of the black swan effect. I suggest all humans listen to this lecture on growth, the University of Colorado At Boulder gave a fantastic talk on growth, what it is, what it isn't, and how humans completely misunderstand it. http://www.youtube.com/watch?v=u5iFESMAU58
Fit a line to the temperature of heated water, once you think you've fit a curve, a black swan happens, and the water boils. This effect happens all throughout our universe, and your primitive function (new-old)/old is not going to help you.
Here is Java code that accomplishes most of the above notions in a neat package that suits my needs:
Critter growth - (a critter can be "radio waves", "beetles", "oil temprature", "stock options", anything).
public double evaluate_critter_growth_return_a_gain_percentage(
double old_value, double new_value) throws Exception{
double abs_old = Math.abs(old_value);
double abs_new = Math.abs(new_value);
//This is your shift function, fool around with it and see how
//It changes. Have a full battery of unit tests though before you fiddle.
double biggest_absolute_value = (Math.max(abs_old, abs_new)+1)*2;
if (new_value <= 0 || old_value <= 0){
new_value = new_value + (biggest_absolute_value+1);
old_value = old_value + (biggest_absolute_value+1);
}
if (old_value == 0 || new_value == 0){
old_value+=1;
new_value+=1;
}
if (old_value <= 0)
throw new Exception("This should never happen.");
if (new_value <= 0)
throw new Exception("This should never happen.");
return (new_value - old_value) / old_value;
}
Result
It behaves kind-of sort-of like humans have an instinctual feel for critter growth. When our bank account goes from -9000 to -3000, we say that is better growth than when the account goes from 1000 to 2000.
1->2 (1.0) should be bigger than 1->1 (0.0)
1->2 (1.0) should be smaller than 1->4 (3.0)
0->1 (0.2) should be smaller than 1->3 (2.0)
-5-> -3 (0.25) should be smaller than -5->-1 (0.5)
-5->1 (0.75) should be smaller than -5->5 (1.25)
100->200 (1.0) should be the same as 10->20 (1.0)
-10->1 (0.84) should be smaller than -20->1 (0.91)
-10->10 (1.53) should be smaller than -20->20 (1.73)
-200->200 should not be in outer space (say more than 500%):(1.97)
handle edge case 1-> -4: (-0.41)
1-> -4: (-0.42) should be bigger than 1-> -9:(-0.45)
Simplest solution is the following:
=(NEW/OLD-1)*SIGN(OLD)
The SIGN() function will result in -1 if the value is negative and 1 if the value is positive. So multiplying by that will conditionally invert the result if the previous value is negative.
Percentage growth is not a meaningful measure when the base is less than 0 and the current figure is greater than 0:
Yr 1 Yr 2 % Change (abs val base)
-1 10 %1100
-10 10 %200
The above calc reveals the weakness in this measure- if the base year is negative and current is positive, result is N/A
It is true that this calculation does not make sense in a strict mathematical perspective, however if we are checking financial data it is still a useful metric. The formula could be the following:
if(lastyear>0,(thisyear/lastyear-1),((thisyear+abs(lastyear)/abs(lastyear))
let's verify the formula empirically with simple numbers:
thisyear=50 lastyear=25 growth=100% makes sense
thisyear=25 lastyear=50 growth=-50% makes sense
thisyear=-25 lastyear=25 growth=-200% makes sense
thisyear=50 lastyear=-25 growth=300% makes sense
thisyear=-50 lastyear=-25 growth=-100% makes sense
thisyear=-25 lastyear=-50 growth=50% makes sense
again, it might not be mathematically correct, but if you need meaningful numbers (maybe to plug them in graphs or other formulas) it's a good alternative to N/A, especially when using N/A could screw all subsequent calculations.
You should be getting a negative result - you are dividing by a negative number. If last year was negative, then you had negative growth. You can avoid this anomaly by dividing by Abs(Last Year)
Let me draw the scenario.
From: -303 To 183, what is the percentage change?
-303, -100% 0 183, 60.396% 303, 100%
|_________________ ||||||||||||||||||||||||________|
(183 - -303) / |-303| * 100 = 160.396%
Total Percent Change is approximately 160%
Note: No matter how negative the value is, it is treated as -100%.
The best way to solve this issue is using the formula to calculate a slope:
(y1-y2/x1-x2)
*define x1 as the first moment, so value will be "C4=1"
define x2 as the first moment, so value will be "C5=2"
In order to get the correct percentage growth we can follow this order:
=(((B4-B5)/(C4-C5))/ABS(B4))*100
Perfectly Works!
Simplest method is the one I would use.
=(ThisYear - LastYear)/(ABS(LastYear))
However it only works in certain situations. With certain values the results will be inverted.
It really does not make sense to shift both into the positive, if you want a growth value that is comparable with the normal growth as result of both positive numbers. If I want to see the growth of 2 positive numbers, I don't want the shifting.
It makes however sense to invert the growth for 2 negative numbers. -1 to -2 is mathematically a growth of 100%, but that feels as something positive, and in fact, the result is a decline.
So, I have following function, allowing to invert the growth for 2 negative numbers:
setGrowth(Quantity q1, Quantity q2, boolean fromPositiveBase) {
if (q1.getValue().equals(q2.getValue()))
setValue(0.0F);
else if (q1.getValue() <= 0 ^ q2.getValue() <= 0) // growth makes no sense
setNaN();
else if (q1.getValue() < 0 && q2.getValue() < 0) // both negative, option to invert
setValue((q2.getValue() - q1.getValue()) / ((fromPositiveBase? -1: 1) * q1.getValue()));
else // both positive
setValue((q2.getValue() - q1.getValue()) / q1.getValue());
}
These questions are answering the question of "how should I?" without considering the question "should I?" A change in the value of a variable that takes positive and negative values is fairly meaning less, statistically speaking. The suggestion to "shift" might work well for some variables (e.g. temperature which can be shifted to a kelvin scale or something to take care of the problem) but very poorly for others, where negativity has a precise implication for direction. For example net income or losses. Operating at a loss (negative income) has a precise meaning in this context, and moving from -50 to 30 is not in any way the same for this context as moving from 110 to 190, as a previous post suggests. These percentage changes should most likely be reported as "NA".
Just change the divider to an absolute number.i.e.
A B C D
1 25,000 50,000 75,000 200%
2 (25,000) 50,000 25,000 200%
The formula in D2 is: =(C2-A2)/ABS(A2) compare with the all positive row the result is the same (when the absolute base number is the same). Without the ABS in the formula the result will be -200%.
Franco
Use this code:
=IFERROR((This Year/Last Year)-1,IF(AND(D2=0,E2=0),0,1))
The first part of this code iferror gets rid of the N/A issues when there is a negative or a 0 value. It does this by looking at the values in e2 and d2 and makes sure they are not both 0. If they are both 0 then it will place a 0%. If only one of the cells are a 0 then it will place 100% or -100% depending on where the 0 value falls. The second part of this code (e2/d2)-1 is the same code as (this year - lastyear)/Last year
Please click here for example picture
I was fumbling for answers today, and think this would work...
=IF(C5=0, B5/1, IF(C5<0, (B5+ABS(C5)/1), IF(C5>0, (B5/C5)-1)))
C5 = Last Year, B5 = This Year
We have 3 IF statements in the cell.
IF Last Year is 0, then This Year divided by 1
IF Last Year is less than 0, then This Year + ABSolute value of Last Year divided by 1
IF Last Year is greater than 0, then This Year divided by Last Year minus 1
Use this formula:
=100% + (Year 2/Year 1)
The logic is that you recover 100% of the negative in year 1 (hence the initial 100%) plus any excess will be a ratio against year 1.
Short one:
=IF(D2>C2, ABS((D2-C2)/C2), -1*ABS((D2-C2)/C2))
or confusing one (my first attempt):
=IF(D2>C2, IF(C2>0, (D2-C2)/C2, (D2-C2)/ABS(C2)), IF(OR(D2>0,C2>0), (D2-C2)/C2, IF(AND(D2<0, C2<0), (D2-C2)/ABS(C2), 0)))
D2 is this year, C2 is last year.
Formula should be this one:
=(thisYear+IF(LastYear<0,ABS(LastYear),0))/ABS(LastYear)-100%
The IF value if < 0 is added to your Thisyear value to generate the real difference.
If > 0, the LastYear value is 0
Seems to work in different scenarios checked
This article offers a detailed explanation for why the (b - a)/ABS(a) formula makes sense. It is counter-intuitive at first, but once you play with the underlying arithmetic, it starts to make sense. As you get used to it eventually, it changes the way you look at percentages.
Aim is to get increase rate.
Idea is following:
At first calculate value of absolute increase.
Then value of absolute increase add to both, this and last year values. And then calculate increase rate, based on the new values.
For example:
LastYear | ThisYear | AbsoluteIncrease | LastYear01 | ThisYear01 | Rate
-10 | 20 | 30 = (10+20) | 20=(-10+30)| 50=(20+30) | 2.5=50/20
-20 | 20 | 40 = (20+20) | 20=(-20+40)| 60=(20+40) | 3=60/2
=(This Year - Last Year) / (ABS(Last Year))
This only works reliably if this year and last year are always positive numbers.
For example last_year=-50 this_year = -1. You get -100% growth when in fact the numbers have improved a great deal.