variance formula question

**MercySakesAlive** · 05-07-2018, 11:05 PM

Trying to find the variance of a group of data. Each piece of data occurs at different frequencies.

Is the formula

A. variance = SIGMA (x ² * p) - EV ²

B. variance = SIGMA (x ² -EV ²) * p

x= data point , EV = mean , p = probability', SIGMA = summation

thanks.

**lessj** · 05-08-2018, 12:08 AM

So uh, what are you asking? I could definitely answer whatever it is, gotta be more clear.

**Phoebe** · 05-08-2018, 12:58 AM

**MercySakesAlive** · 05-08-2018, 07:27 AM

Ugh, sorry about that. My exponents weren't superscripted and my formula was meaningless. Thanks, Phoebe. That'll do.

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**Phoebe** · 05-08-2018, 08:06 AM

You're welcome
But I am curious to know what you are doing with.

**Three** · 05-08-2018, 08:10 AM

Originally Posted by MercySakesAlive

Ugh, sorry about that. My exponents weren't superscripted and my formula was meaningless. Thanks, Phoebe. That'll do.

You do realize neither of your formulas were right?

**Three** · 05-08-2018, 08:14 AM

The correct formula says to take the difference between each data point and the mean then square it, and then multiply that by its probability and add all the resulting products together.

Standard deviation would be the square root of the variance.

**MercySakesAlive** · 05-08-2018, 09:09 AM

Yes i see that, Three. Thanks!

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**MercySakesAlive** · 05-08-2018, 10:10 AM

Phoebe, I'm trying to learn how to calculate SD. Right now, just working on a lottery. Only for my amusement and education.

**MercySakesAlive** · 05-08-2018, 01:11 PM

I was trying to analyze a scratch ticket. The ticket cost $1.00.

The expected value is - $0.22.

Standard deviation is $11.60.

I'm confused about how to interpret that. If I buy one ticket for $1.00 my expected value is - $0.22 but my standard deviation says that one standard deviation from the EV means I could lose (- $0.22 - 11.60 or -$0.22 + 11.60)... How can I lose $11.82 when I buy one ticket for $1.00? scratch ticket math.jpg scratch ticket.jpg

**Gronbog** · 05-08-2018, 01:39 PM

A standard deviation of 11.60 does not mean that you can lose $11.82 if the mean is -0.22. It is a measure of the volatility of the expected distribution of results compared to the mean. The relative sizes of -0.22 and 11.60 tell you that, if you play this lottery, you will experience large swings in your results. This is not surprising. You expect long losing streaks of 1 and 0 units between rare but somewhat larger wins.

When applied to a large number of samples, standard deviation can be used to calculate the probability that your actual results are within the expected range.

**MercySakesAlive** · 05-08-2018, 01:51 PM

Solid answer, Gronbog. Thanks for your help.

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**MercySakesAlive** · 05-08-2018, 01:54 PM

Could I apply the Desirability Index or assign a SCORE to a game like this? It seems like I have the necessary components, win rate and SD, but I'm not sure if it would be meaningful.

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