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sd

Anonymous Thu 07 Nov 13:46:04 2019 No.11125026 View Reply Original Report

Quoted By: >>11125040 >>11125713 >>11125796 >>11125828

> Approximately 68% of the data lies within 1 standard deviation from the mean
> Approximately 95% of the data lies within 2 standard deviations from the mean
> Approximately 99.7% of the data lies within 3 standard deviations from the mean

Okay but the fuck does it mean for a whole data set to have a standard deviation of 1/2/3?

Anonymous

Anonymous Thu 07 Nov 2019 13:55:53 No.11125040 Report

Quoted By: >>11125044 >>11125809

>>11125026
68% if your things lie in the range -1<X<1if you standard deviation is 1.

Anonymous

Anonymous Thu 07 Nov 2019 13:58:25 No.11125044 Report

Quoted By: >>11125894

>>11125040
That's always true though isn't it?

Anonymous

Anonymous Thu 07 Nov 2019 18:49:34 No.11125654 Report

Quoted By:

g-guys?

Anonymous

Anonymous Thu 07 Nov 2019 19:21:56 No.11125713 Report

Quoted By: >>11126762

>>11125026
standard deviation can be understood as the mean of "the difference between each data point and the mean".

YOU HAVE JUST BEEN EDUCATED BY AN ARTS DEGREE. KILL YOURSELF IN SHAME SCIENCE BITCH, NOW YOU PLAY A BACH SONATTA

Anonymous

Anonymous Thu 07 Nov 2019 19:59:28 No.11125796 Report

Quoted By: >>11125809

>>11125026
when people make the claim that 95% of the data lies within 2 standard deviations of the mean, "data" refers to the entire population. For example, suppose the height of males was truly normally distributed with a normal distribution of N(175cm, 7.5^2) (mean of 175cm, standard deviation of 7.5cm), then 95% of ALL males have a height between 175 - 2*7.5 and 175 + 2*7.5 (or 160 to 190).

When people refer to a "data set" having a standard deviation, it is referring to the estimate of the standard deviation that we obtain from the data set which should be a SUBSET of our population. Suppose I went and surveyed 8 males, to get an estimate for the mean and the standard deviation, and found heights of: 168, 168, 172, 174, 178, 179, 180, 187. Then the mean of this dataset is 175.75, but the standard deviation is 6.5.

The standard deviation of a data-set is calculated: $\sqrt{\frac{1}{n-1}\sum_{i=1}^n (x_i - \bar{x})^2}$ .
On the other hand, the standard deviation of a population, is simply the square root of the variance, which is a property of the DISTRIBUTION.

Anonymous

Anonymous Thu 07 Nov 2019 20:04:30 No.11125809 Report

Quoted By: >>11125849

>>11125796
Yes both variance and sd are measures of spread. Now it doesn't actually matter much if you're describing a population or a sample -- all you're doing mathematically is taking the average squared distance from the mean -- the only difference between population and sample is whether you divide by N or N - 1.

But all of this is besides the point. What I'm asking is the following. What does it actually mean for data (as a set) to have sd = 1? Is there any special significance or property (like >>11125040
is implying) or is it just an arbitrary number?

Anonymous

Anonymous Thu 07 Nov 2019 20:13:33 No.11125828 Report

Quoted By:

>>11125026
>Okay but the fuck does it mean for a whole data set to have a standard deviation of 1/2/3?
It's on a logarithmic axies

Anonymous

Anonymous Thu 07 Nov 2019 20:21:27 No.11125849 Report

Quoted By: >>11125888

>>11125809
>the only difference between population and sample is whether you divide by N or N - 1.
Yes and no. Yes, if you have a finite population then you divide by N, but the entire idea behind "95% of the data lies in 2 standard deviations of the mean", comes from the approximation to the normal distribution. This is why I was referring to the normal distribution.

The SD is just the (corrected) mean of the squared differences from the sample mean in the case of a sample dataset. The number "95% if that is what you mean, simply comes from the property of the normal distribution, which is that,

$\displaystyle \int_{-2}^2 \frac{1}{\sqrt{2\pi}} e^{-x^2/2} \ dx \simeq 0.95$

Or equivalently,

$\displaystyle \int_{-2\sigma}^{2\sigma} \frac{1}{\sqrt{2\pi} \sigma} e^{\frac{-x^2}{2\sigma^2} } \ dx \simeq 0.95$

If what you are asking, if it matters whether a dataset specifically has a standard deviation of 1 or 2 or 3 it is just arbitrary, we can speak in 1.5 standard devations if we wanted, or 1.123213 standard deviations. The nomenclature comes from that in a normal distribution $N(\mu, \sigma^2)$ , then each " $\sigma$ " is a standard deviation, so that if

Anonymous

Anonymous Thu 07 Nov 2019 20:33:25 No.11125872 Report

Quoted By: >>11125888

the thing you have in green text is true, the values 1/2/3 in your normal text could be literally any values, there's no connection or special property

so if your sd = 1, then the entire normal population is within about 6 units (a bit over 3 to both directions from the mean)

if your sd = 2, double the values above, and so on

Anonymous

Anonymous Thu 07 Nov 2019 20:40:17 No.11125888 Report

Quoted By:

>>11125849
>>11125872
Okay thanks for the explanation. I guess I just have to look at a lot of data to get an intuitive feel for what an sd of 1/2/2.5/etc. actually means in practice.

Anonymous

Anonymous Thu 07 Nov 2019 20:41:37 No.11125894 Report

Quoted By:

>>11125044
If it’s a normal distribution(ie symmetric bell curve) after normalizing you would get the same 1/2/3 rule

Anonymous

Anonymous Fri 08 Nov 2019 03:12:28 No.11126762 Report

Quoted By:

>>11125713
wrong

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