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# Natural Variations: Newsletter Challenge (November 2016)

Posted October 31, 2016 12:00 AM
Pathfinder Tags: challenge questions

This month's Challenge Question: Specs & Techs from IEEE Engineering360:

Natural variations in repeated measurements form a normal distribution. Ten recent measurements are made where the average and standard deviation of the measurement is known from many previous measurements. How many times more likely is it that none of the ten recent measurements will occur outside of 2 standard deviations of the average as compared to outside of 1 standard deviation of the average?

When dealing with normal distributions, the probability of a data point occurring within 1 standard deviation is 68.27%. The probability of a data point occurring within 2 standard deviations is 95.45%. The odds that 10 recent measurements all fall within 1 standard deviation is 0.6827*0.6827*0.6827*0.6827*0.6827*0.6827*0.6827*0.6827*0.6827*0.6827=0.682710=0.022=2.2%

Similarly, the odds that 10 recent measurements all fall within 2 standard deviations is (0.954510=0.6277=62.8%). Since 0.6277/0.022=28.5, it is 28.5 times more likely that ten measurements will fall within 2 standard deviations than 1 standard deviation. This makes sense since 2 standard deviations provides more room for measurement variation than 1 standard deviation.

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#1

### Re: Natural Variations: Newsletter Challenge (November 2016)

10/31/2016 2:33 AM

If you ask todays climate statistics they all will be outside the standard deviation and all will be lower because this is the only way to create a "warming".

I like this little write up.

Never try to walk across a river just because it has an average depth of four feet. Martin Friedman

“Statistics: The only science that enables different experts using the same figures to draw different conclusions.“ Evan Esar

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#7

### Re: Natural Variations: Newsletter Challenge (November 2016)

12/09/2016 1:28 PM

Statistics is also the math that allows for the prediction to be made that, if 18 women get pregnant on the same day, then 1 baby per month may reliably be predicted for the next 18 months. (Isn't it?...)

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#8

### Re: Natural Variations: Newsletter Challenge (November 2016)

12/09/2016 4:34 PM

It depends which of the women you are talking about .

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#9

### Re: Natural Variations: Newsletter Challenge (November 2016)

12/10/2016 11:45 AM

is he talking about a women?

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#10

### Re: Natural Variations: Newsletter Challenge (November 2016)

12/13/2016 1:51 PM

I'm not sure, but it could be that one bloke is very busy.

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#11

### Re: Natural Variations: Newsletter Challenge (November 2016)

12/13/2016 4:18 PM

The point is that none of the resultant babies will (arrive) during the last eight months, no matter how the statistics are interpreted...

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#12

### Re: Natural Variations: Newsletter Challenge (November 2016)

12/15/2016 11:37 AM

In 1945, for example, Beulah Hunter who was 25 at the time gave birth after a pregnancy lasting 375 days

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#13

### Re: Natural Variations: Newsletter Challenge (November 2016)

12/15/2016 11:54 AM

Was there actual (ultrasound, etc.) documentation, or did it just seem like it took that long to her?...

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#14

### Re: Natural Variations: Newsletter Challenge (November 2016)

12/15/2016 12:08 PM

The date makes it look a bit suss, though extended pregnancies do seem to happen. The snippet was just the first one I glanced at here.

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#15

### Re: Natural Variations: Newsletter Challenge (November 2016)

12/19/2016 11:54 AM

Aren't you then talking about ''the exception that proves the rule''...

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#16

### Re: Natural Variations: Newsletter Challenge (November 2016)

12/20/2016 5:26 PM

Very much, but that's why we have bell curve graphs ? I'd suggest that it's so those odd anomalies are included in the data set.

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#17

### Re: Natural Variations: Newsletter Challenge (November 2016)

12/22/2016 12:30 PM

You certainly have the right to choose to miss the point...

However, one extended pregnancy longer than 1 day short of 10 months is, say, one chance in a million live births, which statistically, is zero percent, to at least 5 decimal places...

And therefore, is within the margin-of-error of +/- 0.000005...

Thus, statistically speaking, zero babies would be born during the last eight of 18 months...

Thereby demonstrating that statistics can be (ab)used to make physically ridiculous conclusions, and that is the point...

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#18

### Re: Natural Variations: Newsletter Challenge (November 2016)

12/22/2016 7:49 PM

I'm going to tell my mommy about you.

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#2

### Re: Natural Variations: Newsletter Challenge (November 2016)

10/31/2016 10:00 AM

Let me just ask my mentor....

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### Re: Natural Variations: Newsletter Challenge (November 2016)

10/31/2016 10:31 AM

Probability that 1 measurement occurs inside 1 sigma: .341 x 2 = .682

Probability that 1 measurement occurs inside 2 sigma: .477 x 2 =.954

Probability that 10 measurements all occur inside 1 sigma: (.682)10

Probability that 10 measurements all occur inside 2 sigma: (.954)10

Ratio of probabilities = (.954/.682)^10 =28.684

https://en.wikipedia.org/wiki/Standard_deviation

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#4

### Re: Natural Variations: Newsletter Challenge (November 2016)

11/02/2016 3:50 AM

When we have the answer, I wonder if it can be applied to all posts made to the question.

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#5

### Re: Natural Variations: Newsletter Challenge (November 2016)

11/09/2016 1:04 PM

OH, WOW... That's hilarious. Good work, friend. haha

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#6

### Re: Natural Variations: Newsletter Challenge (November 2016)

11/17/2016 10:08 PM

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