Mass Lottery Statistical Analysis
is 'Technical Stuff' relating to the methods employed to produce your data package.
Statistical Analysis
Descriptive Statistics
allow us to describe groups of many numbers. One way to do this is by reducing them to a few numbers that are typical of the groups, or describe their characteristics. The average is one kind of descriptive statistic. Measures of spread are another kind.Statistical Significance
in general, is a way of estimating the likelihood that a difference between two samples indicates a real difference between the populations from which the samples are taken, rather than being due purely to chance. If a result is very unlikely to have arisen we say it is statistically significant. If a result would only arrive by chance once in a hundred times, we would call it significant. If only once in 1,000 times, it would be highly significant. If once in twenty times, only probably significant. Now as far as the lottery is concerned, statistical significance is expressed in terms of probability. I. e, each number will probably be draw within a certain range and so, the probability of you winning the jackpot without this data is highly unlikely and, your ability to pick the winning numbers on a regular basis with this data is highly significant!Frequency Distribution
A frequency distribution is an arrangement of a group of numbers in a pattern that shows how frequently each occurs. This is done by grouping the numbers and arranging them in a table according to size. For example,1, 1
2, 2, 2
3, 3, 3, 3
4, 4, 4, 4, 4
5, 5, 5, 5, 5, 5
6, 6, 6, 6, 6
7, 7, 7, 7
8, 8, 8
9, 9
Using Frequency Distribution, one can spot trends in each game. The way the number hits are distributed in each game is a good indicator of how numbers will continue to be distributed. Totaling these distributions, one can clearly see where and when numbers may repeat. Within the data package you receive, you will find this data displayed in a highly useful and very easy to understand manner.
Combinations and Permutations
A Combination is the selection of a number of items from a larger number in which the order of selection does not matter.
For example, if we have five items, how many ways can we select three from the five if we are not bothered about what order the items appear in?
We will call the five items A,B,C,D,E
We can now set them out to show that there are ten ways in which they can be combined in groups of three.
ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE.
Permutation is the selection of a number of items from a larger number when the order the items appears in does matter.
For example, ABC, ACB, BAC, BCA, CAB and CBA are all the same combination, because they contain the same three items, but they are six different permutations, because the items are in a different order.
Understanding the 'Standard' odds
To understand how lottery odds are calculated we first need to understand probability. Probability tells us how many times a particular number or combination of numbers should occur over time.
To simplify this example we will use a single dice cube as an example.
If you were to roll a dice what would be the chances of rolling, say a two? Because there are 6 possible numbers that could be rolled on the single dice and since only one of them can appear on a single roll then you have 1 chance in 6 (1/6). Pretty easy so far!
Now lets work out the odds of a combination of different numbers occurring?
What would be the chances of rolling a two or a six? In this case the chances of rolling a two are 1/6 and the chances of rolling a six are 1/6. Therefore you simply ADD the two outcomes: 1/6 + 1/6 = 2/6 or 1/3. Therefore the chances are 1 in 3 of rolling either a 3 or 6. Still pretty simple.
What would be the odds of rolling a two on two consecutive rolls of the dice? In this case the odds are MULTIPLIED together. Thus we have 1/6 × 1/6 = 1/36. Thus the chances of rolling a two on 2 consecutive rolls is 1 chance in 36.
Ok, So how does this work with the lottery?
The calculations are the same; we simply expand the above theory.
If we select 6 numbers and the game has 50 numbers in the pool the odds are calculated as follows.
* The odds of having the first number drawn are simply 6 in 50 (6/50).
* Since we have already picked one of our six numbers and there is one less number in the pool that can be picked, then there are only five of a possible 49 numbers left in the pool that can be drawn. Therefore the odds of having the second number drawn is 5 in 49 (5/49).
* Since we now have four of our six picks left and there are now only 48 balls left in the pool to be drawn, the chances of getting the third is 4 in 48 (4/48).
* We now have three of our six picks left and only 47 balls left in the pool to be drawn. Therefore the chances of getting the forth number is 3 in 47 (3/47).
* With two of our six picks left and only 46 balls left in the pool. The chances of getting the fifth number are 2 in 46 (2/46).
* With only one of our six picks left and only 45 balls left in the pool, the chances of getting the last number is 1 in 45 (1/45).
To calculate the odds of picking all six numbers we multiply the individual odds together to get the overall odds: 6/50 × 5/49 × 4/48 × 3/47 × 2/46 × 1/45 = 720/11,441,304,000 or 1/15890700 (1 chance in 15.89 million).
The standard formula used to calculate odds is as follows:
Odds = Fac(x) ÷ [Fac(n) × Fac(x - n)].
What the variables mean are;
* Fac( ) means factorial, which means multiplying a number out by all of itsfactors. For example Fac(6) would be 6 x 5 x 4 × 3 × 2 × 1 = 720
* x = the number of balls in the game pool (in the above example, 50).
* n = the numbers allowed to be chosen (in above example, 6).
Thus in a 6/50 lotto the odds as follows:
Odds = Fac(50) ÷ [ Fac(6) × Fac(50-6)] = 1/15,890,700: the same as the longhand calculation performed above.
The Fact Is It's Nearly Impossible To Win The Mass Lottery Without This Data!
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