Benford's Law

[MeaMaximaCulpa]

I said on a thread about tipping that I had other/better things to do than continue that specific discussion. (Tropo you are right, I should just not bothered posting/reading any further).

Anyway, so here is one of the other (better?) ways to use my time. I guess I am competing with our dear Weho now, but of course, I can not touch that guy, he is the number one. Where is he btw?

But check out this Benford and his "law" about how the digit 1 appears as the first digit in many instances, much more often than the other digits. Actually 2-9 shows an ever decreasing probability.

See Google or Wikipedia for more info if you are interested. I found it facinating. But then again, it does not take much to facinate such a small and sodden brain...

As for Thailand related, I guess not a lot, other than that the law applies also here, just look around you and see. My house street number, car registration, neighbour's car registration, credit card bonus points and I am sure a host of other numbers start with a one. Unfortunately my electricity bill tends to start with a 5 or 6, but now I am seeing the first 4 in a long time.

Also it could be used to check accounting practices and tax returns (Mr T anyone?), government statistics and voting results, seeing we are approaching the election in Thailand. It appears that people falsifying numerical data tend to distribute the initial digits much more evenly between 1 and 9 than if the figures are true. So Benford's Law is actually used in forensic accounting. Have fun!

[Scott]

My mother was an accountant many years ago and one of the tricks she used for finding out if there were transposed numbers was to divide the total by 9. If it was divisible, then most likely two numbers were inverted. I have no idea how that works, but she swore by it.

[JetsetBkk]

I just read the Wikipedia article on it, and now my brain hurts.

I'll have another go later!

[MeaMaximaCulpa]

Hi guys,

Thanks for replying, I didn't think anyone was as nerdy as yours truly. But encouraging to see someone is at least trying...

Scott, my g/f is in the finance and accounting field, and she seems to have heard about the divide by 9 rule, but also could not tell me exactly what it is or does or why it does it. I shall ask her to find out more, and if she does, I shall report back the findings. But she is very busy these days, so don't hold your breath.

JetsetBkk, if your head hurts, what about my head? I think the Wikipedia article was good, but a bit heavy. I have a few other little gems hidden away for later, if it turns out there is a market for suchlike.

Again thanks for stopping by Nerds 'R Us. Welcome back anytime!

[JetsetBkk]

Hi guys,

Thanks for replying, I didn't think anyone was as nerdy as yours truly. But encouraging to see someone is at least trying...

Scott, my g/f is in the finance and accounting field, and she seems to have heard about the divide by 9 rule, but also could not tell me exactly what it is or does or why it does it. I shall ask her to find out more, and if she does, I shall report back the findings. But she is very busy these days, so don't hold your breath.

JetsetBkk, if your head hurts, what about my head? I think the Wikipedia article was good, but a bit heavy. I have a few other little gems hidden away for later, if it turns out there is a market for suchlike.

Again thanks for stopping by Nerds 'R Us. Welcome back anytime!

Yes, please updates us with the divide by 9 rule. I could get my head around that one even less than old Benford's Law! I need a good night's rest before I tackle them again.

[DavidOxon]

the divide by 9 rule is easy to use

it's a way of realising transposed number and the

difference in value between them. It only applies to numbers

switched in addition for example

adding 21 in a column instead of 12.

as these two digits are only one away from each other, the the amount

the sum will be out is 1 x 9 or 9.

if the two digits are 2 numbers away from each other eg 35 and 53

the difference will be 18 and so on.

SO! if you are adding up a sequence of numbers and the answer is wrong by a factor of 9,

then look for which multiple of 9 it is (1-9) and then look for pairs of numbers

that many apart.

David

[JetsetBkk]

the divide by 9 rule is easy to use <snip>

Thanks for that excellent explanation!

[tropo]

Thanks for replying, I didn't think anyone was as nerdy as yours truly. But encouraging to see someone is at least trying...

You're probably about to get a shock. I'm probably nerdier.

I'm suprised they made the prevalence of the digit '1' a law and gave it a name. It was probably someone who needed to make a name for themselves. I say this because it is intuitive that numbers starting with the digit '1' would be the most common and obviously it would taper off as the numbers became greater. I didn't need Benford to tell me that.

Googling numbers can give you a good idea of which numbers are more common:

These are google hits (today) for common numbers:

4,880,000,000 for 0

8,790,000,000 for 1

8,040,000,000 for 2

7,760,000,000 for 3

5,770,000,000 for 4

5,500,000,000 for 5

4,820,000,000 for 6

4,680,000,000 for 7

4,400,000,000 for 8

4,120,000,000 for 9

5,810,000,000 for 10

5,010,000,000 for 11

4,700,000,000 for 12

4,400,000,000 for 13

4,590,000,000 for 14

4,800,000,000 for 15

4,490,000,000 for 16

4,300,000,000 for 17

4,620,000,000 for 18

3,990,000,000 for 19

4,730,000,000 for 20

4,010,000,000 for 21

4,220,000,000 for 22

4,060,000,000 for 23

3,870,000,000 for 24

3,970,000,000 for 25

3,750,000,000 for 26

3,860,000,000 for 27

3,740,000,000 for 28

3,390,000,000 for 29

4,580,000,000 for 30

3,020,000,000 for 31

2,120,000,000 for 32

2,220,000,000 for 33

1,990,000,000 for 34

2,140,000,000 for 35

1,990,000,000 for 36

1,820,000,000 for 37

1,930,000,000 for 38

1,860,000,000 for 39

2,460,000,000 for 40

884,000,000 for 61 (first number with under 1 billion hits)

1,010,000,000 for 66 (makes a brief come back)

1,370,000,000 for 70 (for some reason this one is more popular)

1,120,000,000 for 75 (and this one too)

1,400,000,000 for 80 (another popular one)

1,390,000,000 for 90 (and again over 1 billion hits)

2,340,000,000 for 100 (as expected - last with over 2 billion hits)

478,000,000 for 102 (first under half-billion)

628,000,000 for 110

766,000,000 for 120

537,000,000 for 125

514,000,000 for 130

859,000,000 for 150

504,000,000 for 160

516,000,000 for 180

1,160,000,000 for 200 (last with over 1 billion hits)

713,000,000 for 250

881,000,000 for 300

652,000,000 for 400

996,000,000 for 500

562,000,000 for 600

681,000,000 for 800

878,000,000 for 1000 (last over half-billion)

...and just in case you maybe wondering...

6,710,000,000 for the letter 'a'

Google wouldn't give me a total for '.' so we can only guess at which is the most common character on the Internet.

Edited November 30, 2007 by tropo

[sinom]

That must be the "nerdiest" thread killer I've ever seen !

well done!