standard deviation for 649 sum

[Bertil]

Suppose I can examine 13984 draws of the 6/49 lotto and then
tabulate the frequencies for each sum, I would ideally find each frequency to be 0.1% of the theoretical.
E.g. the sum 150 would have come up 166 times, sum 125
would have occurred 127 times, the sum 100 would have come
up 56 times and the sum 75 would have occurred 12.6 times.

But each of these numbers would have a statistical deviation.
By what formula could I predict the std.dev. for each sum?
Available data indicate that the spread is a very small fraction
of the theoretical for sum 150 but very large for the sum 75.
No doubt there is a formula to explain this. Can somebody
please tell me what formula applies.

Bertil

 

[Bertil]

Unless I'm greatly mistaken, the std.dev. will be equal to the square root of the expected frequency at any level.
If somebody disagrees, please speak up.

Bertil

 

[PAB]

Hi Bertil,

I Don't Know if this will be of Any Help.
I Calculate the Standard Deviation ( in Excel ) for the Frequency of Numbers Drawn in a 649 Lotto.
If we Assume the Numbers 01 to 49 are in Cells B7:B55 & the Total Number of Times Drawn are in Cells C7:C55, then in Cell C57 for Example Enter the Formula :-
=STDEVPA(C7:C55)

The Array Formula ( Entered with Ctrl-Shift-Enter to give you the Curly Brackets {} at EACH End of the Formula ) which Builds the Answer Step by Step is :-
=SQRT((SUM(((C7:C55)^2)*COUNT(C7:C55))-SUM(C7:C55)^2)/COUNT(C7:C55)^2)

Hope this Helps.
All the Best.
PAB

 

[peter]

Excuse me for butting in here, but could someone explain to me what use is it in knowing the standard deviation? how does this help in number selection? Thank you.

 

[Bertil]

standard devation

Excuse me for butting in here, but could someone explain to me what use is it in knowing the standard deviation? how does this help in number selection? Thank you.

The search for a formula for the std.dev. was motivated by mathematical curiosity, but not intended as a guide in playing.

Bertil

 

[troller]

Wow!

NEVER MIND

 

[PAB]

Hi Peter,

Excuse me for butting in here, but could someone explain to me what use is it in knowing the standard deviation? how does this help in number selection? Thank you.

I Saw this Strategy Mentioned Somewhere a While Ago Now ( Can't Remember where ) and did some Research on it. Like Bertil, I was Motivated by Mathematical Curiosity, and thought that it could be Used in Some Way Towards a Filter for the Reduction of Combinations. Perhaps Somebody Else has Managed to come up with a Workable Use for Standard Deviation in Respect to the Lotto, if they have, Perhaps they could Post their Findings to Share with the Rest of us.
This is Something that GillesD Might be Able to Shed some Light on.

All the Best.
PAB

 

[Bertil]

standard deviation in lotto

There are three separate std.dev. one can use for lotto.

In his book "Lottery Numbers Past, Present and Future" Harry Schneider used two as a filter to weed out "unlikely" combinations. He based his analysis on only two sets of 50 draws.
That was a much too small sample . He tested the s.d between the sums and also the s.d. within the sums. He worked with 649.
In addition I posted the s.d. for the frequencies of the sums.
Maybe the latter could be used to test if the drawings are biased.

Bertil

 

[Bertil]

std.dev.

PAB offered a program for calculating the s.d but I'm unable to
take advantage of it due to lack of any ability of any kind to
implement any program. So I wonder if PAB would just list the
s.d. for each of the hypothetical sums I mentioned. Then I
would be able to compare the results to my simple method.

Bertil

 

[Nick Koutras]

Variance=((N-1)*(N+1))/12

SD=Sqrt(Variance)


For a 6/49 game SD=14.14

 

[Bertil]

standard deviation

Nick Koutras suggested that the std.dev. be calcualed by a formula, that seem s to be derived from the formula for the std.dev. for the sums, which is (N+1)n(N-n)/12. but there is no known agreement for this use. It happens to approximate the
emirical value obtained from a large sample in some cases but
far from all.

Bertil