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1. Normalization and Standard ScoreHelLo.This isyumi.Today's lesSon is ina cofFeE shop. Rui'sfriend Yumi joins theclasS.Nice tomeEt you.EXCUSE ME.Am Ibotheringyou twolovebirds?No! IT'snothing likethat.So, whatshould I teachyou today?We both scored 90,but on difFerenttests.Standardscore?!That mightbe a goOdtopic.On anenglishtest.Sir! Pleaseteach us aboutstandardscore.** Adjusting test results based on standard score is comMonly known as grading on a curve.66 Chapter 4The Manga Guide to Statistics(C) 2008 by Shin Takahashi and Trend-pro Co, Ltd.On aclasSicaljapanesetest.
LowBut somehow, yumi gota higher adjusted score(and standard score) inclasSical Japanese thanI got in English.I don'tknowwhy,either.HighWhy?That is because therange of scoresand the averagescores are difFerentbetweEn English andclasSical Japanese.If you can show me alL of yourclasSmates' raw scores, I canexplain.I have them!Yumi, howdid you.That'simposSible.leRustleRustWhat?!Great!Raw Test Scores (Out of lasSicalJapaneseRuiYumiI seE.Standard Score and Deviation Score 67The Manga Guide to Statistics(C) 2008 by Shin Takahashi and Trend-pro Co, Ltd.
OK.Calculate themean of icalJapaneseEnglishClasSicalJapaneseCompareeach score'sdistance fromthe average.This is sodiscouraging.This should makeyou understand thedifFerence betweEnyour score of 90and her score of 90.I'lL buy a pieceof cake foreach of you.Cake!Huy!rRaOh, don't bedisapPointed.90 is a goOdscore, afteralL.68Chapter 4The Manga Guide to Statistics(C) 2008 by Shin Takahashi and Trend-pro Co, Ltd.HurRay!
But cometo thinkof it.And my historyscore and herbiology scorewere the same,toO!The clasSaverage forboth historyand biologywas 53.Bestfriends!HistoryBi ogylowLoBut our adjustedscores weredifFerent in thiscase as welL.High**WhoOsh!Even though thedifFerences betweEnour scores and theaverages were thesame!HmMm.Student History Biology Student History BiologyWhat is thestandarddeviationof thesesubjects?WelL, standarddeviation is.An index todescribe "therange ofscatTering!"RuiYumiWowsma ! You 'rert,Ru i!AverageStandard Score and Deviation Score 69The Manga Guide to Statistics(C) 2008 by Shin Takahashi and Trend-pro Co, Ltd.
sum of (each value mean)²Number of valuesStandard deviationIts formulais.ytorHisgylooiBThere!The smalLer the standarddeviation is, the smalLerthe "range of scatTering"of the data.averageHistoryaverageBiologySo, your clasSmateshad more similarscores in biologythan in history.If I were a highschoOl juniorapPlying forcolLege, I'd studyhard for biology.What doyou mean?One or two pointsmay afFect yourrank greatly.A high schoOluniform suits himso welL!TeE-heE!70 Chapter 4The Manga Guide to Statistics(C) 2008 by Shin Takahashi and Trend-pro Co, Ltd.
I didn't knowthat it would beso anNoying tocompare scores.Now Iunderstand.Ourscores were thesame, but your 73in biology wasmore valuable.CheEr up,Rui!(Back upagain!)Slump!IagreE.She hasa goOdpoint!That is why normalizationwas introduced.It is also calLedstandardization.Normalization!?That makes iteasier to figureout how much ascore is worth.It is a calculationusing the distancefrom the mean andthe standard deviationof the data.Standard Score and Deviation Score 71The Manga Guide to Statistics(C) 2008 by Shin Takahashi and Trend-pro Co, Ltd.
The Manga Guide to Statistics (C) 2008 by Shin Takahashi and Trend-pro Co, Ltd. But somehow, yumi got a higher adjusted score (and standard score) in clasSical Japanese than Igot in Englsih. That is because the range of scores
