THE NORMAL THING

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  1. The Normal Thing In Government Crossword
  2. The Normal Thing About The Jacksons
  3. Normal Things Under A Microscope
  4. How To Make Slime With The Normal Things
  5. The Normal Theater
  6. The Normal Tarot
  7. Bloomington Normal Activities

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Nor·mal

(nôr′məl)
A town of central Illinois near Bloomington. It is the seat of Illinois State University, founded as a normal school in 1857.

nor·mal

(nôr′məl)adj.
1. Conforming with, adhering to, or constituting a norm, standard, pattern, level, or type; typical: normal room temperature; one's normal weight; normal diplomatic relations.
2. Biology Functioning or occurring in a natural way; lacking observable abnormalities or deficiencies.
3. Chemistry
a. Relating to or designating the normality of a solution.
b. Abbr. n Designating an aliphatic hydrocarbon having an acyclic unbranched chain of carbon atoms.
4. Mathematics
b. Perpendicular to the direction of a tangent line to a curve or a tangent plane to a surface.
5. THE NORMAL THING
a. Relating to or characterized by average intelligence or development.
n.
1. The usual, expected, or standard state, form, amount, or degree: Temperatures have been above normal for this time of year.
2. Mathematics A perpendicular, especially a perpendicular to a line tangent to a plane curve or to a plane tangent to a space curve.
[Middle English, from Late Latin normālis, from Latin, made according to the square, from norma, carpenter's square; see gnō- in Indo-European roots.]
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

normal

(The normal order of thingsˈnɔːməl) adj
1. usual; regular; common; typical: the normal way of doing it; the normal level.
2. constituting a standard: if we take this as normal.
3. (Psychology) psychol
a. being within certain limits of intelligence, educational success or ability, etc
4. (Biology) biologymed (of laboratory animals) maintained in a natural state for purposes of comparison with animals treated with drugs, etc
5. (Chemistry) chem (of a solution) containing a number of grams equal to the equivalent weight of the solute in each litre of solvent. Symbol: N
6. (Chemistry) chem denoting a straight-chain hydrocarbon: a normal alkane. Prefix: n-, e.g. n-octane
7. (Mathematics) geometry another word for perpendicular1
n
8. the usual, average, or typical state, degree, form, etc
10. (Mathematics) geometry a line or plane perpendicular to another line or plane or to the tangent of a curved line or plane at the point of contact
[C16: from Latin normālis conforming to the carpenter's square, from norma norm]
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

nor•mal

(ˈnɔr məl)
adj.
1. conforming to the standard or the common type; usual; regular; natural.
3. of natural occurrence.
4. approximately average in any psychological trait, as intelligence, personality, or emotional adjustment.
6. free from disease or malformation.
7.
a. being at right angles, as a line; perpendicular.
b. of the nature of or pertaining to a mathematical normal.
8.
a. (of a solution) containing one equivalent weight of the constituent in question in one liter of solution.
b. pertaining to an aliphatic hydrocarbon having a straight unbranched carbon chain, each carbon atom of which is joined to no more than two other carbon atoms.
n.
9. the normal form or state; the average or mean.
11.
a. a perpendicular line or plane, esp. one perpendicular to a tangent line of a curve, or a tangent plane of a surface, at the point of contact.
b. the portion of this perpendicular line included between its point of contact with the curve and the x-axis.
nor•mal′i•ty,n.
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
Noun1.normal - something regarded as a normative example; 'the convention of not naming the main character'; 'violence is the rule not the exception'; 'his formula for impressing visitors'
convention, rule, pattern, formula
practice - knowledge of how something is usually done; 'it is not the local practice to wear shorts to dinner'
mores - (sociology) the conventions that embody the fundamental values of a group
code of behavior, code of conduct - a set of conventional principles and expectations that are considered binding on any person who is a member of a particular group
universal - a behavioral convention or pattern characteristic of all members of a particular culture or of all human beings; 'some form of religion seems to be a human universal'
Adj.1.normal - conforming with or constituting a norm or standard or level or type or social norm; not abnormal; 'serve wine at normal room temperature'; 'normal diplomatic relations'; 'normal working hours'; 'normal word order'; 'normal curiosity'; 'the normal course of events'
sane - mentally healthy; free from mental disorder; 'appears to be completely sane'
standard - conforming to or constituting a standard of measurement or value; or of the usual or regularized or accepted kind; 'windows of standard width'; 'standard sizes'; 'the standard fixtures'; 'standard brands'; 'standard operating procedure'
abnormal, unnatural - not normal; not typical or usual or regular or conforming to a norm; 'abnormal powers of concentration'; 'abnormal amounts of rain'; 'abnormal circumstances'; 'an abnormal interest in food'
2.normal - in accordance with scientific laws
paranormal - not in accordance with scientific laws; 'what seemed to be paranormal manifestations'
3.normal - being approximately average or within certain limits in e.g. intelligence and development; 'a perfectly normal child'; 'of normal intelligence'; 'the most normal person I've ever met'
psychological science, psychology - the science of mental life
abnormal - departing from the normal in e.g. intelligence and development; 'they were heartbroken when they learned their child was abnormal'; 'an abnormal personality'
4.normal - forming a right angle
geometry - the pure mathematics of points and lines and curves and surfaces
perpendicular - intersecting at or forming right angles; 'the axes are perpendicular to each other'
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.

normal

adjective
1.usual, common, standard, average, natural, regular, ordinary, acknowledged, typical, conventional, routine, accustomed, habitual, run-of-the-millThe two countries have resumed normal diplomatic relations.The hospital claimed they were simply following their normal procedure.
usualrare, unusual, remarkable, exceptional, peculiar, abnormal, irregular, uncommon, singular, unnatural
2.sane, reasonable, rational, lucid, well-adjusted, compos mentis(Latin), in your right mind, mentally sound, in possession of all your facultiesDepressed patients are more likely to become ill than normal people.
Collins Thesaurus of the English Language – Complete and Unabridged 2nd Edition. 2002 © HarperCollins Publishers 1995, 2002

normal

adjectiveCommonly encountered:
average, common, commonplace, general, ordinary, typical, usual.
The American Heritage® Roget's Thesaurus. Copyright © 2013, 2014 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
normální
normaalisäännöllinen
normalan
normal; eîlilegur, venjulegur
普通の
normali būklėnormaliai
normaalnormalegewonegewoon
normal

normal

[ˈnɔːməl]A.ADJ
1. (= usual) → normal
it's perfectly normal to feel that wayes muynormalsentirse así, no hay nada raro en sentirse así
above/below normalpor encima/debajo de lo normal
to carry on as normalseguirhaciendo todo como de costumbre
to get backorreturn to normal [situation] → normalizarse, volvera lanormalidad
'normal service will be resumed as soon as possible'se reanudará la emisión lo antes posible
I woke at the normal timeme desperté a la horade siempre
he bought a return ticket instead of the normal singlecompró un billete de ida y vuelta en vezdel de sóloida que solía comprar
3. (= healthy) [baby] → normal; [pregnancy] → sin complicaciones
B.CPDnormal schoolN (US) (o.f.) → escuelafnormal
Collins Spanish Dictionary - Complete and Unabridged 8th Edition 2005 © William Collins Sons & Co. Ltd. 1971, 1988 © HarperCollins Publishers 1992, 1993, 1996, 1997, 2000, 2003, 2005

normal

[ˈnɔːrməl]adj
(not out of the ordinary)normal(e)
a normal car → une voiturenormale
to lead a normal life → mener une vienormale
in normal circumstances, under normal circumstances → en tempsnormal
to continue as normal →
worse than normal → pire que d'habitude
(= habitual) [place, time] → habituel(le)
at the normal time → normal time
n
to get back to normal [situation, person, family] →
to return to normal [weather, conditions] → redevenirnormal(e)
Collins English/French Electronic Resource. © HarperCollins Publishers 2005

normal

adj
normal; (= customary)üblich; it’s a perfectly or quite a normal thingdas ist völlignormal; it’s perfectly normal for you to feel that wayes ist vollkommennormal, dass Sie so empfinden; it’s normal practicedas ist so üblich; normal temperature/consumption/outputNormaltemperaturf/-verbrauchm/-leistungf; normal view (Comput) → Normalansichtf; he is not his normal self todayer ist heute so anders; a higher than normal risk of infectionein Infektionsrisiko, das über dem Normalenliegt
(Chem) normal solutionNormallösungf
n no pl (of temperature)Normalwertm, → Durchschnittm; (Math) → Senkrechtef; (to tangent) → Normalef; temperatures below normalTemperaturen unter dem Durchschnitt; her temperature is below/above normalsie hat Untertemperatur/erhöhte Temperatur; when things/we are back to or return to normalwenn sich alles wiedernormalisiert hat; just carry on as normalmachen Sie einfachnormalweiter; life went on as normaldas Lebengingnormalweiter
Collins German Dictionary – Complete and Unabridged 7th Edition 2005. © William Collins Sons & Co. Ltd. 1980 © HarperCollins Publishers 1991, 1997, 1999, 2004, 2005, 2007

normal

[ˈnɔːml]
1.adjnormale
it was quite normal for him to object → era perfettamentenormale che obiettasse
it is perfectly normal to be left-handed → è perfettamentenormaleornaturale essere mancini
2.n
a.to return to normaltornare alla normalità
above/below normal → al disopra/al disotto della norma
Collins Italian Dictionary 1st Edition © HarperCollins Publishers 1995

normal

(ˈnoːməl) adjective
usual; without any special characteristics or circumstances. How much work do you do on a normal day?; normal people; His behaviour is not normal. gewone, normale عادي، طَبيعي нормален normal normální gewöhnlich normal κανονικός, φυσιολογικόςnormal normaalne معمولی normaali normalרגיל सामान्य, प्रकृत normalan, uobičajen normális, rendes normal normal; eðlilegur, venjulegur normale 普通の 보통의 normalus, įprastas normāls, parasts biasa normaalnormalnormalny عادى normal nor­mal, obişnuit обыкновенный; обычный normálny navaden normalan normal, vanlig ปกติ normal 平常的,正常的 нормальний, звичайний حسب معمول، عام bình thường 平常的,正常的
norˈmality (-ˈmӕ-) noun
normaliteit وَضْع طَبيعي أو إعْتِيادي нормалност normalidade normálnost die Normalität normalitet ομαλότητα, φυσιολογική κατάσταση normalidad normaalsus حالت عادى normaalius normalité נוֹרמָלִיוּת सामान्य स्थिति normalnost, redovitost szabályosság kenormalan eðlilegt ástand normalità 正常 정상임 normali būklė, padėtis norma, normāls stāvoklis keadaan yang biasa normaliteit det normale, normaltilstandnormalność عادى normalidade normalitate нормальность; обычное состояние normálnosť normalnost normalnost normaltillstånd ความปกติ normallik 正常 нормальність; звичайний стан عام حالت trạng thái bình thường 正常
normally adverb
1. in a usual, ordinary way. He was behaving quite normally yesterday. gewone بِصورةٍ عادِيَّه нормално normalmente normálně normal normalt φυσιολογικάnormalmente normaalselt معمولا؛ بطور عادى normaalisti normalement בְּאוֹפֶן נוֹרמָאלִי सामान्यत: normalno, obično rendes körülmények között secara biasa venjulega normalmente 普通に 정상적으로 normaliai normāli; parasti secara normal normaalnormaltnormalnie په عادى توګه normalmente nor­mal нормально; как обычно normálne normalno uobičajeno normalt โดยปกติ normal olarak 正常地 нормально طبعي طور پر thông thường 正常地
2. usually; most often. I normally go home at 4 o'clock. gewoonlik عادَةً، غالبا обикновено normalmente obvykle gewöhnlich normalt συνήθως, κανονικάnormalmente tavaliselt اکثر اوقات tavallisesti normalementבדרך כלל लम्ब रूम में, नियमित या सामान्य ढ़ग से obično rendszerint biasanya vanalega normalmente 普通は 보통 dažniausiai, paprastai parasti biasanya gewoonlijknormalt, vanligvis, som regelzazwyczaj اكثره وخت normalmente de obicei обычно obyčajne navadno obično i vanliga fall, vanligtvis โดยปกติ genellikle 通常 зазвичай عموماً như thường lệ 一般
Kernerman English Multilingual Dictionary © 2006-2013 K Dictionaries Ltd.

normal

عَادِيّ normální normal

The Normal Thing In Government Crossword

normalομαλόςnormal normaalinormal normalannormale 普通の 정상의normaalnormalnormalnynormalобычный normal ปรกติnormal bình thường正常的
Multilingual Translator © HarperCollins Publishers 2009

nor·mal

English-Spanish Medical Dictionary © Farlex 2012

The Normal Thing About The Jacksons

  • How long will it take by regular mail? (US)
    How long will it take by normal post? (UK)
Collins Multilingual Translator © HarperCollins Publishers 2009
English-Spanish/Spanish-English Medical Dictionary Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.

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Data can be 'distributed' (spread out) in different ways.

It can be spread out
more on the left

Or more on the right
Or it can be all jumbled up

But there are many cases where the data tends to be around a central value with no bias left or right, and it gets close to a 'Normal Distribution' like this:

A Normal Distribution

The 'Bell Curve' is a Normal Distribution.
And the yellow histogram shows some data that
follows it closely, but not perfectly (which is usual).

It is often called a 'Bell Curve'
because it looks like a bell.

Many things closely follow a Normal Distribution:

  • heights of people
  • size of things produced by machines
  • errors in measurements
  • blood pressure
  • marks on a test

We say the data is 'normally distributed':

The Normal Distribution has:

  • mean = median = mode
  • symmetry about the center
  • 50% of values less than the mean
    and 50% greater than the mean

Quincunx

You can see a normal distribution being created by random chance!

It is called the Quincunx and it is an amazing machine.

Have a play with it!

Standard Deviations

The Standard Deviation is a measure of how spread out numbers are (read that page for details on how to calculate it).

When we calculate the standard deviation we find that generally:

68% of values are within
1 standard deviation of the mean

95% of values are within
2 standard deviations of the mean

99.7% of values are within
3 standard deviations
of the mean

Example: 95% of students at school are between 1.1m and 1.7m tall.

Normal Things Under A Microscope

Assuming this data is normally distributed can you calculate the mean and standard deviation?

The mean is halfway between 1.1m and 1.7m:

Mean = (1.1m + 1.7m) / 2 = 1.4m

95% is 2 standard deviations either side of the mean (a total of 4 standard deviations) so:

1 standard deviation= (1.7m-1.1m) / 4
= 0.6m / 4
= 0.15m

And this is the result:

It is good to know the standard deviation, because we can say that any value is:

  • likely to be within 1 standard deviation (68 out of 100 should be)
  • very likely to be within 2 standard deviations (95 out of 100 should be)
  • almost certainly within 3 standard deviations (997 out of 1000 should be)

Standard Scores

The number of standard deviations from the mean is also called the 'Standard Score', 'sigma' or 'z-score'. Get used to those words!

Example: In that same school one of your friends is 1.85m tall

You can see on the bell curve that 1.85m is 3 standard deviations from the mean of 1.4, so:

Your friend's height has a 'z-score' of 3.0

It is also possible to calculate how many standard deviations 1.85 is from the mean

How far is 1.85 from the mean?

It is 1.85 - 1.4 = 0.45m from the mean

How many standard deviations is that? The standard deviation is 0.15m, so:

0.45m / 0.15m = 3 standard deviations

So to convert a value to a Standard Score ('z-score'):

  • first subtract the mean,
  • then divide by the Standard Deviation

And doing that is called 'Standardizing':

We can take any Normal Distribution and convert it to The Standard Normal Distribution.

Example: Travel Time

A survey of daily travel time had these results (in minutes):

26, 33, 65, 28, 34, 55, 25, 44, 50, 36, 26, 37, 43, 62, 35, 38, 45, 32, 28, 34

The Mean is 38.8 minutes, and the Standard Deviation is 11.4 minutes (you can copy and paste the values into the Standard Deviation Calculator if you want).

Convert the values to z-scores ('standard scores').

To convert 26:

then divide by the Standard Deviation: −12.8/11.4 = −1.12

So 26 is −1.12 Standard Deviations from the Mean

Here are the first three conversions

Original ValueCalculationStandard Score
(z-score)
26(26-38.8) / 11.4 =−1.12
33(33-38.8) / 11.4 =−0.51
65(65-38.8) / 11.4 =+2.30
.........

And here they are graphically:

You can calculate the rest of the z-scores yourself!

The z-score formula that we have been using is:

  • z is the 'z-score' (Standard Score)
  • x is the value to be standardized
  • μ ('mu') is the mean
  • σ ('sigma') is the standard deviation

And this is how to use it:

Example: Travel Time (continued)

Here are the first three conversions using the 'z-score formula':

z = x − μσ

  • μ = 38.8
  • σ = 11.4
xx − μσz
(z-score)
2626 − 38.811.4= −1.12
3333 − 38.811.4= −0.51
6565 − 38.811.4= +2.30
.........

The exact calculations we did before, just following the formula.

Why Standardize ... ?

It can help us make decisions about our data.

Example: Professor Willoughby is marking a test.

Here are the students' results (out of 60 points):

20, 15, 26, 32, 18, 28, 35, 14, 26, 22, 17

Most students didn't even get 30 out of 60, and most will fail.

The test must have been really hard, so the Prof decides to Standardize all the scores and only fail people more than 1 standard deviation below the mean.

The Mean is 23, and the Standard Deviation is 6.6, and these are the Standard Scores:

-0.45, -1.21, 0.45, 1.36, -0.76, 0.76, 1.82, -1.36, 0.45, -0.15, -0.91

Now only 2 students will fail (the ones lower than −1 standard deviation)

Much fairer!

It also makes life easier because we only need one table (the Standard Normal Distribution Table), rather than doing calculations individually for each value of mean and standard deviation.

In More Detail

Here is the Standard Normal Distribution with percentages for every half of a standard deviation, and cumulative percentages:

Example: Your score in a recent test was 0.5 standard deviations above the average, how many people scored lower than you did?

  • Between 0 and 0.5 is 19.1%
  • Less than 0 is 50% (left half of the curve)

So the total less than you is:

50% + 19.1% = 69.1%

In theory 69.1% scored less than you did (but with real data the percentage may be different)

A Practical Example: Your company packages sugar in 1 kg bags.

When you weigh a sample of bags you get these results:

  • 1007g, 1032g, 1002g, 983g, 1004g, ... (a hundred measurements)
  • Mean = 1010g
  • Standard Deviation = 20g

Some values are less than 1000g ... can you fix that?

The normal distribution of your measurements looks like this:

31% of the bags are less than 1000g,
which is cheating the customer!

It is a random thing, so we can't stop bags having less than 1000g, but we can try to reduce it a lot.

Let's adjust the machine so that 1000g is:

  • at −3 standard deviations:
  • From the big bell curve above we see that 0.1% are less. But maybe that is too small.
  • at −2.5 standard deviations:
  • Below 3 is 0.1% and between 3 and 2.5 standard deviations is 0.5%, together that is 0.1% + 0.5% = 0.6% (a good choice I think)

So let us adjust the machine to have 1000g at −2.5 standard deviations from the mean.

Now, we can adjust it to:

How To Make Slime With The Normal Things

  • increase the amount of sugar in each bag (which changes the mean), or
  • make it more accurate (which reduces the standard deviation)

Let us try both.

Adjust the mean amount in each bag

The Normal Theater

The standard deviation is 20g, and we need 2.5 of them:

2.5 × 20g = 50g

So the machine should average 1050g, like this:

Adjust the accuracy of the machine

Or we can keep the same mean (of 1010g), but then we need 2.5 standard deviations to be equal to 10g:

10g / 2.5 = 4g

The Normal Tarot

So the standard deviation should be 4g, like this:

Bloomington Normal Activities

(We hope the machine is that accurate!)

Or perhaps we could have some combination of better accuracy and slightly larger average size, I will leave that up to you!

More Accurate Values ...

Use the Standard Normal Distribution Table when you want more accurate values.

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