Math Is Fun Forum

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

ones in natural data

OK. This is interesting.
I'm asking you to explain something, but if someone knows it - don't tell!
There's an amazing fact - in statistical data tables, the number 1 is first digit almost 35% of the cases!
You may think this is not true.
But wait a minute - i'm not lying you!
I'm asking you to explain this strange phenomenom.

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IPBLE:  Increasing Performance By Lowering Expectations.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: ones in natural data

I've seen this before.
The more general fact is that the probability that the first digit of a random number in a data table will be x is log[sub]10[/sub](x+1) - log[sub]10[/sub]x.

Very interesting stuff.

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Why did the vector cross the road?
It wanted to be normal.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: ones in natural data

1/0.1 is 10
1/0.1999 is about 5
So from .1 to .1999, the reciprocal of numbers from 5 to 10 start with a 1.
And
1/.333333 is 3
1/.444444 is 9/4 or 2.25
1/.555555 is 9/5 or 1.80
That is one idea.

Also if the numbers in the data table are from 1 to say 40, and counting numbers, then
1, 10, 11... 19 start with one, and that's eleven out of 40 numbers, or 27.5 % of them.

Am I on the right track??

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igloo myrtilles fourmis

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: ones in natural data

Is that a theoretical or experimental probability?

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: ones in natural data

theoretically-experimental - agrees with the theory AND with the experiments.

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IPBLE:  Increasing Performance By Lowering Expectations.