# Powerball winning numbers Содержание

## Statistical : object

Kind: global namespace

• :

### Statistical.μ(freq) ⇒

Calculate arithmetic mean of ball-count

Kind: static method of Returns: — Arithmatic Mean of weights

Param Type Description
freq A single ball-frequency array from

Example (Get Arithmetic Mean of Red Balls)
var f = powerball.frequencies(winners)
console.log(powerball.μ(f.red))
Example (Get Arithmetic Mean of White Balls)
console.log(powerball.mean(f.white))

### Statistical.gmean(freq) ⇒

Calculate geometric mean of ball-count

Kind: static method of Returns: — Geometric Mean of weights

Param Type Description
freq A single ball-frequency array from

Example (Get Geometric Mean of Red Balls)
var f = powerball.frequencies(winners)
console.log(powerball.gmean(f.red))
Example (Get Geometric Mean of White Balls)
console.log(powerball.gmean(f.white))

### Statistical.median(freq) ⇒

Calculate median of ball-count

Kind: static method of Returns: — Median of weights

Param Type Description
freq A single ball-frequency array from

Example (Get Median of Red Balls)
var f = powerball.frequencies(winners)
console.log(powerball.median(f.red))
Example (Get Median of White Balls)
console.log(powerball.median(f.white))

### Statistical.range(freq) ⇒

Calculate range of ball-count

Kind: static method of Returns: — High/low range of numbers for weights.

Param Type Description
freq A single ball-frequency array from

Example (Get Range of Red Balls)
var f = powerball.frequencies(winners)
console.log(powerball.range(f.red))
Example (Get Range of White Balls)
console.log(powerball.range(f.white))

### Statistical.σ(freq) ⇒

Calculate standard deviation of ball-count

Kind: static method of Returns: — Standard Deviation of weights

Param Type Description
freq A single ball-frequency array from

Example (Get Standard Deviation of Red Balls)
var f = powerball.frequencies(winners)
console.log(powerball.stddev(f.red))
Example (Get Standard Deviation of White Balls)
console.log(powerball.σ(f.white))

## Theoretical Prediction Versus The Actual Results Of The U.S. Powerball (Odd-Even pattern analysis as of February 05, 2020)

In Mathematics, we compute the expected frequency of each pattern by multiplying the probability by the number of draws.

Expected Frequency = Probability X number of draws

There are 449 draws in Powerball from October 7, 2015, to February 05, 2020. So, in the case of a 3-odd-2-even pattern, we get 146.69320621 by multiplying 0.326710926970499 by 449.

We round off the number to arrive at 147. Now we see that the 3-odd-2-even pattern is expected to occur about 147 times in 449 draws.

Doing similar computation with the rest of the odd-even patterns, we will come up with the following complete comparison table below:

Patterns Expected frequency in 449 draws Actual frequency in 449 draws
3-odd-2-even 147 148
2-odd-3-even 142 138
4-odd-1-even 71 75
1-odd-4-even 65 61
5-odd-0-even 13 14
0-odd-5-even 11 13

Looking at the table, the close value between expected frequency and actual frequency proves that Powerball behaves in a predictable pattern.

A different way to say it is that Powerball lotto follows the dictate of probability.

Fortunately for you as a lotto player, you can take advantage of this probability principle to get the best shot possible. Thanks to mathematics.

Using the probability formula, we can predict how specific number composition will likely occur in a lottery draw.

For example, probability calculation shows that a 3-odd-2-even pattern is expected to appear 147 times. In the actual draw, the same pattern occurred 148 times. Very close prediction.

If you look at the whole graph, it doesn’t take a second to realize that prediction and actual results closely agree together.

As a Powerball player, you may want to put your money on the best two patterns. And as a smart player, you don’t want to waste your money on all-even-number or all-odd-number.

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