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Stig Holmquist
science forum beginner

Joined: 30 Apr 2005
Posts: 48

Posted: Sun Jul 02, 2006 2:33 pm    Post subject: Digit frequency variation in a lottery

Drawing the winning numbers XYZ in a pick 3 type lottery is done by
random selection of one numbered ball out of ten from each of three
containers. Each ball is supposed to have an equal chance of being
drawn.

After 1000 draws in a recent state lottery only a few balls,digits,
were drawn 100 times, while the rest were drawn from 79 to 124 times.
In the first position,X, the digit frequencies varied from 82 to 113,
in the second position,Y, they varied from 79 to 109 and in the third
position,Z, they varied from 85 to 124.

The frequency std.dev. for position X was 11.53, for Y it was 9.75
and for Z 11.45. For all 3000 draws the over all std.dev. was 10.56
for 30 sets. But each digit was drawn on average 300 times with a
std.dev. of 11.75, because the totals for the ten digits varied from
276 to 314.

The expected binomial std.dev. for 1000 draws is 9.5 but for
3000 draws it would be 16.43. So why was the actual value
only 11.76? Does it imply a bias? Very long term draws, such as
10 000, were not available and one would like to test for short term
bias if any.

Is my statistical analysis correct?

Stig Holmquist

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