#normal distribution

[aceofstars1]

Reblog for sample size yadda yadda <3

[paris-suggestion]

i found a stopwatch on the floor of the engine room and i like it cause it helps me keep track of the time dilation + lately as a game i will start it randomly to see how many minutes i can go without anything going wrong. my high score is 00:21:03.

[oediex]

"What is normal?"

That was the question at the philosophy café today. It is chosen from a series of questions proposed by the participants and then voted on.

It seemed a silly because easily-answered question to me. Normal is, very simply, that which is the norm. It is the way most people are or behave or think. It is that which is typical. It's Gaussian distribution.

The notion of normal is problematic only because it is often seen as inherently good. Desirable. Worthy. When one is abnormal, something is wrong with you. This seems to still be the predominant line of thinking.

I see normality as a mere fact. It is normal to not be mentally ill, because most people aren't mentally ill. It is normal to own a car, because most people own a car. It's statistics. It's neutral. There is no value judgement attached when I call something normal.

Sometimes when people ask me why I'm not wearing shoes, I will tell them it's healthy. They will nod in agreement. If a kid asks me, I will tell them it is fun. This is an instant win. But every now and then, when I feel like it, I will tell people I'm just weird.

Kids will laugh at that and shrug, but adults will practically trip over their own feet in their haste to assure me that I am not. At no point do they consider that maybe, just maybe, I don't mind being weird. Maybe I even like it.

I'm always so struck by the fact that people seem to think I want to be normal. That everyone wants to be normal.

I guess it's normal to want to be normal. And that's okay. It's just a fact after all. No value judgement from my side, no sir. None at all.

[sparseposter]

intuition for the central limit theorem

the central limit theorem is a frankly magical theorem. i'll assume everyone reading this post is familiar with it, i'm speedrunning out my thoughts, i don't want to spend too much time on this. but basically yeah why should everything add up to the normal distribution? why should the mean of basically everything be normal?

so this bothered me for a long time, it was always kinda insane. i learned about it, and then a while later i learned how to prove it, but i still didn't get it. but then i watched some 3B1B videos (all kudos to them btw) and then specifically i saw this one comment on a video and it all clicked.

basically: what's so special about the normal distribution? like, why *that* one in particular?

well, there's this other property of normal distributions, which may seem unrelated at first but is actually the key to the whole thing: if you add two normal distributions, you get another normal distribution.

and this is the key to the whole thing! because it means that, when you're doing sums of random variables, normal variables are a *fixed point*.

so at least for me this instantly finally made everything click - things converging to fixed points is just so incredibly natural, it comes up everywhere. to go into a little more detail, distributions where if you add two of them together you get a third one of the *same type* are called stable distributions, and it turns out that the normal distribution is special among stable distributions because it's the unique one with finite mean and variance - all the others, Cauchy, Levy, etc. don't satisfy this condition. i don't understand why but yeah. so then it makes intuitive sense that - if you keep averaging lots and lots and lots of variables which have finite means and variances together and converge to anything at all - it *must* be to the only fixed point which has finite mean and variance: the normal distribution.

[i-iii-iii-vii]

[in-sightpublishing]

On High-Range Test Construction 4: Iakovos Koukas on Understanding IQ Test Scores

                  Publisher: In-Sight Publishing Publisher Founding: March 1, 2014 Web Domain: http://www.in-sightpublishing.com Location: Fort Langley, Township of Langley, British Columbia, Canada Journal: In-Sight: Independent Interview-Based Journal Journal Founding: August 2, 2012 Frequency: Three (3) Times Per Year Review Status: Non-Peer-Reviewed Access: Electronic/Digital & Open…

[mathmedicine]

AS LEVEL STATISTICS 1 (PAPER 5)

STATISTICS 1 (2002-2010) C1 Representation of Data C2 Permutations and Combinations C3 Probability C4 Discrete Random Variables C5 The Normal Distribution

[mr-avocado-man7]

“i hope to become a kid who is loved…”

[yuviur]

Summer vacation, 4am.

Tons of easter eggs in this one! Click the image to find them (and for better quality ofc)

Close ups and process shots under the cut, description in alt text

[normal-dist-polls]

This poll is loosely normally distributed!

Your are the monarch of a historical/fantasy kingdom, who perished many years ago and your name is only written down in recorded history, know only to future generations.

Out of the 130 options in the picker wheel here (all are gender neutral),

And yes: there is a 'no epithet' option in there.

I got The Oathtaker.

[clumsypuppy]

littlest furth shop

@laikascomet

[summergoodwife]

not to tell you how to pilot your helicopter but i think the vast majority of you draw John Gaius too conventionally attractive. he's very pointedly just a guy apart from the freaky eyes.

[1nk20ul]

Discovering Jon and Martin’s Birthdays

It’s a wonder how much you can uncover about The Magnus Archives using only a bit of mathematics and a smidge of psychology.

Apparently I have too much time for both and can definitively say that I have revealed the absolute best and most accurate dates for both of their birthdays. Feel free to join me as we dissect piece by piece when these two were born and put to rest the age old question: What is Jon’s zodiac sign?

I’ll put the results in the tags as a TLDR if you’re not interested in reading my method and simply care about what star sign they are or what date to put in your calendar so you can go out for ice cream.

Statement Begins.

To find out the birthdays of Jon and Martin, we first must determine when exactly they joined the Archives. This will be important for the wider picture, as after all, the earliest possible birthday must take place after they start working there. We also must understand the Archive team’s speed in order to understand how to space out our statements and find that aforementioned number.

Gertrude Robinson passed away, according to her file, on the 15th of May 2015. This makes 15th May our earliest possible starting date. The next time the day’s date was specified was on 13th January 2016, when Naomi Herne gave a live statement. This is MAG 13, and our latest start date. Obviously, these numbers are nowhere close to the day we’re looking for, but they act as upper and lower limits. Our answer is somewhere inside.

In Jon’s supplemental notes for MAG 12, he states that Gerard Keay passed away late the previous year. Since Gertrude died after Gerard in early 2015, he must have died in late 2014. This confirms that MAG 1-12 was recorded to tape in 2015. We know that MAG 13, the next statement, was given live on 13th January 2016. This creates, at the very least, an almost two-week gap between archiving statements. This is likely due to the holiday season, so the time between 24th December and up to 1st January can be omitted. To recap, MAG 1-12 was recorded in 2015, and MAG 13 onwards in 2016.

The key to determining archival speed lies with Martin. Martin goes missing right before MAG 17 and reappears at the end of MAG 21. As he gave such a detailed account of those two weeks, our archiving timeline can be significantly accurate. MAG 19-20 were more than likely recorded on the same day, meaning three separate recording sessions took place in two weeks. However, it took a minimum of six weeks to record MAG 14-16.

So far, the timeline looks like this:

Now we have to figure out the left half.

Calculating the average time it takes to archive statements from MAG 13-22 (removing any outliers from our calculations), we can find a true average and apply it to the 2015 year. By March of The Magnus Institute’s 2016 calendar year, the Archive staff was able to archive 1.31 statements per week. I double-checked this number by doing the same with the statements recorded between MAG 22 and MAG 39. By multiplying the average amount of weeks it should take them by the adjusted number of statements recorded, it should equal the number of weeks it actually did take them. If the numbers are the same, the average is reliable. Hoping for the number 20, the number of weeks I had calculated... was 20.11. This average seems relievingly trustworthy and fits Elias’ complaint about the staff “barely getting through one statement per week.”

All we have to do now is multiply the first 12 statements by the 1.31 average to determine how many weeks it most likely took to do the recorded work of 2015. This leaves us with 15.72 weeks and makes the earliest and most probable start date somewhere around 5th September 2015. I will round this to 1st September as I am not expecting the team to start working on statements right out the gate, so these extra four days act as a buffer for everyone to get their bearings and find the tape recorder. Also, it’s convenient for Elias’ financials to start everyone on the 1st of the month.

Now is the fun part - the birthdays. We now know that Jon and Martin’s birthdays must fall somewhere between early September and the end of February. Since March kicks off the Archives living with the threat of Jane Prentiss, they have to take place before then. After that point, the team is far too stressed to have the carefree party heard in MAG 161. We also know that Martin’s birthday has to come before Jon’s, as the team mentions going out for ice cream at Jon’s party. This event has to be long enough in the past for Jon to forget about it, so their birthdays must be reasonably spaced out from one another in the allotted time. Likewise, an amount of time must have passed after their start date for the team to be close enough bond to want to celebrate Martin’s birthday.

Martin’s birth year is easy to determine. Martin tells us his age in MAG 56. His birthday could not have happened at this point in 2017, so his birth year must be 1987. In a Q&A, it was speculated that Jon and Martin have birthdays near each other (and one being slightly older than the other), so only 1987 and 1988 are our options for Jon’s birth year. Let’s look a bit closer at that.

Early ‘88 is closer to Late ‘87 than Early ‘87. At Jon’s birthday party, he says he’s turning 38. Martin is 29 at this time. The obvious conclusion to me is that Jon simply adds a decade to his age. (I find this the most hilarious yet believable scenario.) Jonny was also born in 1988, being 28 himself when that scene would take place. As Jon’s childhood details sometimes mirror Jonny’s, I am taking this as a sign of accuracy.

And by doing some additional work that I will not share here, I can reliably say that these are the best observed birthdays for Jon and Martin:

Martin - 23rd November, 1987

Jonathan - 2nd February, 1988

Also, this makes Martin a potential Valentine’s Day Baby. Do with that what you will.

Thanks for reading!

(Full timeline for those who are interested:)

[maybecoffeemixed]

Happy little Trevenants.

[corcjell]

what they look like 2 me