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mancoub · 6 years ago

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Hero's Algorithm

Hero or Heron had an algorithm in the first century that is just great!

I've used this algorithm and variations to solve several irrational problems quickly.

My most recent interest is when you use mixed fractions in place of decimal approximations to find ratios.

The formula is simple enough. When you guess close to the square root of a number g you can divide the number n by g to get another close approximation. Take the average of the two, first g and then n/g and you get a closer approximation. Then substitute that as a new guess g and repeat the process as many times as you can before you run out of CPU or precision.

In these examples I'll stop when the numerator reaches 3-digits

Case 2:

g is 3/2 (1.5)

n/g is 4/3

sum is 9/6 + 8/6 or 17/6

avg is 17/12 (1.41,67)

--------

g2 is 17/12

ng2 is 24/17

sum2 is 289/204 + 288/204

avg2 is 577/408 (1.41421,56)

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Case 3:

g is 9/5 (1.8)

ng is 15/9 or 5/3

sum is 27/15 + 25/15

avg is 52/30 or 26/15 (1.73,3)

--------

g2 is 26/15

ng2 is 45/26

sum2 is 676/390 + 675/390

avg2 1351/780 (1.73205,128)

It's so simple, I'm shocked they don't teach this in schools.

I want to do case 2 again but this time with a far worse guess of 1

Case 2 (part B):

g is 1

ng is 2

sum is 1 + 2

avg is 3/2

So in this case we don't guess very close but we only lose one iteration since our solution is actually our original guess of 1.5

And for a ludicrous guess

Case 2 (part C)

g is 22/7

ng is 14/22

sum is 484/154 + 98/154

avg is 582/308 or 291/154 (1.88)

--------

g2 is 291/154

ng2 is 308/291

sum2 84681/89628+ 47432/89628

avg2 132113/89628 (1.4,740)

The better the guess the more efficient each iteration of the algorithm but even if the guess is way off, eventually it will get back on track.

What’s interesting is that some starting guesses yield very concise results. Or ratios with small numerators and denominators that give many digits of precision.

Martin Gardner in, “Aha! Gotcha: Paradoxes to Puzzle and Delight”, wrote a story called, “The Amazing Code”, about an alien traveler that must return home after visiting Earth. He wants to bring all the world’s knowledge but due to the size of his personal craft and the laws of faster than light travel. He cannot bring anything that weighs more than 2 pounds (my paraphrase from memory, of course). He asks that the entire works of all human knowledge be converted into a single text file and then that text file converted into binary file and then that binary file converted into a single integer. Then he uses his supercomputer to calculate a ratio of two numbers that will reproduce the entire integer as a decimal number between 0 and 1. Once he has the numerator and denominator he then takes out a bar of metal, one that he carried with him from his planet for this very purpose. He uses extremely precise tools to carve a notch in the bar so that when he goes back to his home planet and measures the length left of the notch and then divides it by the measurement of the length to the right of the notch, he will get a decimal number that when converted into an integer can be converted into a binary file and then text to retain all the information he was given.

Gardner explains in this exercise that the bar would have to be made from something so inert that it would not lose atoms in the traveling process because the notch would have to be accurate to the atomic level. Still, it may not be able to record anywhere close to the amount of information stated in this story.

Another mathematician once stated that to get a number of digits of precision for encryption, as the story above suggests, that you would need at least the same number of digits summed between the numerator and denominator. Meaning that you can’t actually get more information from a ratio.

This proposition is only true with completely random, if not transcendental numbers, and there is plenty of evidence like 1/7 which yields a six digit pattern encoded in only two digit ratio. But these are specific cases and you can’t count on this for most data sets.

Bringing it back to Hero’s Method, we can find ratios of irrational numbers like the square root of 2 and we can find higher precision approximations using various methods by hand but we still struggle to store this large amount of information in smaller packages.

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natesafety · 4 years ago

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Congrats to former NATE Chairman Jim Tracy on his Class of 2021 induction into the prestigious Wireless Hall of Fame! We are proud of you! (at Mandarin Oriental, Washington D.C.) https://www.instagram.com/p/CWKWD7-AVg2/?utm_medium=tumblr

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imakuni · 2 years ago

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also got 9th in avg2, 97th in mystery (but knocking out griffybones lol), and 2nd in asuka 120% limitover (i don't wanna talk about that loss rn)

i got fifth in sailor moon at combo breaker

shouts out to this top 8 graphic

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ladmob · 4 years ago

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https://au.ladmobly.com/aVg2

WCGW when you really don't brain your environment? - amazing

WCGW when you really don’t thoughts your surroundings? – awesome

Source

#Halirious, #Problems, #Bahahaha, #PllFunnyHumor

#CruelHumor #Halrious #HilariousPictures #Lololololol #Stupidness

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shiraishi-blog-blog · 4 years ago

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キメラのレシピ1

//@version=4 // This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/

strategy("Y-Profit Maximizer Strategy with Exit Points", shorttitle="Y-PMax Strategy with Exit Points", overlay=true, default_qty_type=strategy.cash, default_qty_value=10000, initial_capital=10000, currency=currency.USD, commission_value=0.1, commission_type=strategy.commission.percent) baslik1 = input(title="-------------------- PMax Setttings -------------------", defval=false) src = input(hl2, title="Source") Periods = input(title="ATR Length", type=input.integer, defval=10) Multiplier = input(title="ATR Multiplier", type=input.float, step=0.1, defval=3.0) mav = input(title="Moving Average Type", defval="ZLEMA", options=["SMA", "EMA", "WMA", "TMA", "VAR", "WWMA", "ZLEMA", "TSF"]) length =input(13, "Moving Average Length", minval=1) changeATR= input(title="Change ATR calculation Method?", type=input.bool, defval=true) showsupport = input(title="Show Moving Average?", type=input.bool, defval=false) showsignalsk = input(title="Show Buy sell signals?", type=input.bool, defval=true) showsignalsc = input(title="Show Price/Pmax cross signals?", type=input.bool, defval=false) highlighting = input(title="Cloud On/Off?", type=input.bool, defval=false)

baslik4 = input(title="-------------------- T3 Setttings --------------------", defval=false) length1 = input(89, "T3 Length") length2 = input(5, "T3 Filter Length") a1 = input(0.84, "T3 Volume Factor") a13 = 0.84 length12 = input(5, "Fibo T3 Length") a12 = input(0.618, "T3 Fibo Volume Factor") T31Show = input(title="Show T3?", type=input.bool, defval=false) T32Show = input(title= "T3 Filter On/Off?", type=input.bool, defval=false) T3FiboLine = input(false, title="T3 Fibonacci Lines?")

shownum = true

baslik7 = input(title="---------------- Take Profit Setttings --------------", defval=false)

len = input(25, "Snake Length") domcycle = input(20, minval=10, title="Dominant Cycle Length") rapida = input(8, "Fast Avg") lenta = input(26, "Slow Avg") stdv = input(0.8, "Length") tpfiltre = input(false, title="TP Filter avg2/avg4?") tplevelshow = input(false, title="TP Level and Exit Level Count On/Off?") tp1show = input(false, title="Early TP Signals On/Off ?")

baslik8 = input(title="------------------- MOST Setttings ------------------", defval=false)

src_most=input(close,"Source") AP2 = input(defval=8,title="Length",minval=1) AF2 = input(defval=2,title="Percent",minval=0.1)/100 mav1 = input(title="Moving Average Type", defval="ZLEMA", options=["VAR","ZLEMA"]) plotbuysell = input(true, "Buy/Sell Shapes On/Off ?", input.bool)

///T3 1&2 e1 = ema((high + low + 2 * close) / 4, length1) e2 = ema(e1, length1) e3 = ema(e2, length1) e4 = ema(e3, length1) e5 = ema(e4, length1) e6 = ema(e5, length1) c1 = -a1 * a1 * a1 c2 = 3 * a1 * a1 + 3 * a1 * a1 * a1 c3 = -6 * a1 * a1 - 3 * a1 - 3 * a1 * a1 * a1 c4 = 1 + 3 * a1 + a1 * a1 * a1 + 3 * a1 * a1 T3 = c1 * e6 + c2 * e5 + c3 * e4 + c4 * e3

e13 = ema((high + low + 2 * close) / 4, length2) e23 = ema(e13, length2) e33 = ema(e23, length2) e43 = ema(e33, length2) e53 = ema(e43, length2) e63 = ema(e53, length2) c13 = -a13 * a13 * a13 c23 = 3 * a13 * a13 + 3 * a13 * a13 * a13 c33 = -6 * a13 * a13 - 3 * a13 - 3 * a13 * a13 * a13 c43 = 1 + 3 * a13 + a13 * a13 * a13 + 3 * a13 * a13 T33 = c13 * e63 + c23 * e53 + c33 * e43 + c43 * e33

///PMax

atr2 = sma(tr, Periods) atr= changeATR ? atr(Periods) : atr2 valpha=2/(length+1) vud1=src>src[1] ? src-src[1] : 0 vdd1=src<src[1] ? src[1]-src : 0 vUD=sum(vud1,9) vDD=sum(vdd1,9) vCMO=nz((vUD-vDD)/(vUD+vDD)) VAR=0.0 VAR:=nz(valpha*abs(vCMO)*src)+(1-valpha*abs(vCMO))*nz(VAR[1]) wwalpha = 1/ length WWMA = 0.0 WWMA := wwalpha*src + (1-wwalpha)*nz(WWMA[1]) zxLag = length/2==round(length/2) ? length/2 : (length - 1) / 2 zxEMAData = (src + (src - src[zxLag])) ZLEMA = ema(zxEMAData, length) lrc = linreg(src, length, 0) lrc1 = linreg(src,length,1) lrs = (lrc-lrc1) TSF = linreg(src, length, 0)+lrs getMA(src, length) => ma = 0.0 if mav == "SMA" ma := sma(src, length) ma

if mav == "EMA" ma := ema(src, length) ma

if mav == "WMA" ma := wma(src, length) ma

if mav == "TMA" ma := sma(sma(src, ceil(length / 2)), floor(length / 2) + 1) ma

if mav == "VAR" ma := VAR ma

if mav == "WWMA" ma := WWMA ma

if mav == "ZLEMA" ma := ZLEMA ma

if mav == "TSF" ma := TSF ma

if mav == "T3" ma := T3 ma ma

MAvg=getMA(src, length) longStop = MAvg - Multiplier*atr longStopPrev = nz(longStop[1], longStop) longStop := MAvg > longStopPrev ? max(longStop, longStopPrev) : longStop shortStop = MAvg + Multiplier*atr shortStopPrev = nz(shortStop[1], shortStop) shortStop := MAvg < shortStopPrev ? min(shortStop, shortStopPrev) : shortStop dir = 1 dir := nz(dir[1], dir) dir := dir == -1 and MAvg > shortStopPrev ? 1 : dir == 1 and MAvg < longStopPrev ? -1 : dir PMax = dir==1 ? longStop: shortStop

///MOST zxLag1 = AP2/2==round(AP2/2) ? AP2/2 : (AP2 - 1) / 2 zxEMAData1 = (src_most + (src_most - src_most[zxLag1])) ZLEMA1 = ema(zxEMAData1, AP2)

valpha1=2/(AP2+1) vud2=src_most>src_most[1] ? src_most-src_most[1] : 0 vdd2=src_most<src_most[1] ? src_most[1]-src_most : 0 vUD1=sum(vud2,9) vDD1=sum(vdd2,9) vCMO1=nz((vUD1-vDD1)/(vUD1+vDD1)) VAR1=0.0 VAR1 := nz(valpha1*abs(vCMO1)*src_most)+(1-valpha1*abs(vCMO1))*nz(VAR1[1])

getMA1(src, length) => ma1 = 0.0 if mav1 == "VAR" ma1 := VAR1 ma1

if mav1 == "ZLEMA" ma1 := ZLEMA1 ma1

Trail1 = getMA1(src, length) SL2 = Trail1*AF2 // Stop Loss

Trail2 = 0.0 Trail2 := iff(Trail1>nz(Trail2[1],0) and Trail1[1]>nz(Trail2[1],0),max(nz(Trail2[1],0),Trail1-SL2),iff(Trail1<nz(Trail2[1],0) and Trail1[1]<nz(Trail2[1],0),min(nz(Trail2[1],0),Trail1+SL2),iff(Trail1>nz(Trail2[1],0),Trail1-SL2,Trail1+SL2)))

Buy = crossover(Trail1, Trail2) Sell = crossunder(Trail1, Trail2) SR=(iff(Trail1 > Trail2 ,1, iff(Trail2 > Trail1,-1,0)))

////T3 TILLSON 1

col1 = T3 > T3[1] col3 = T3 < T3[1] col4 = T33 > T33[1] col5 = T33 < T33[1] color_1 = col1 ? color.green : col3 ? color.red : color.yellow color_4 = col4 ? color.green : col5 ? color.red : color.yellow

e12 = ema((high + low + 2 * close) / 4, length12) e22 = ema(e12, length12) e32 = ema(e22, length12) e42 = ema(e32, length12) e52 = ema(e42, length12) e62 = ema(e52, length12) c12 = -a12 * a12 * a12 c22 = 3 * a12 * a12 + 3 * a12 * a12 * a12 c32 = -6 * a12 * a12 - 3 * a12 - 3 * a12 * a12 * a12 c42 = 1 + 3 * a12 + a12 * a12 * a12 + 3 * a12 * a12 T32 = c12 * e62 + c22 * e52 + c32 * e42 + c42 * e32

col12 = T32 > T32[1] col32 = T32 < T32[1]

///TP BB ve SNAKE

h = ema(high, len) l = ema(low, len)

hp = h / h[len] lp = l / l[len]

avg = avg(hp, lp)

havg = ema(highest(avg, len), len) lavg = ema(lowest(avg, len), len)

avg2 = avg(havg, lavg) avg3 = avg(havg, avg2) avg4 = avg(havg, avg3)

dif = havg - avg2

ust = havg + dif alt = lavg - dif

///BB on MACD

SDev = 0.0 banda_supe = 0.0 banda_inf = 0.0 m_rapida = ema(close,rapida) m_lenta = ema(close,lenta) BBMacd = m_rapida - m_lenta Avg = ema(BBMacd,9) SDev := stdev(BBMacd,9) banda_supe := Avg + stdv * SDev banda_inf := Avg - stdv * SDev

color2 = col12 ? color.blue : col32 ? color.purple : color.yellow

TS1 = plot(Trail1, "ExMov", style=plot.style_line,color=Trail1 > Trail2 ? color.blue : color.yellow, linewidth=2) TS2 = plot(Trail2, "Most", style=plot.style_line,color=Trail1 > Trail2 ? color.green : color.red, linewidth=2)

tp1 = tpfiltre ? crossunder(BBMacd,banda_supe) and (avg>avg2) and (MAvg>PMax) and nz(MAvg[10]) > nz(PMax[10]) : crossunder(BBMacd,banda_supe) and (avg>avg4) and (MAvg>PMax) and nz(MAvg[15]) > nz(PMax[15]) plotshape(tp1 and tp1show, title="TP1", text="TP1", location=location.abovebar, style=shape.labeldown, size=size.tiny, color=color.aqua, textcolor=color.white,transp=0)

plot(T31Show ? T3 : na, color=color_1, linewidth=3, title="T3") plot(T32Show ? T33 : na, color=color_4, linewidth=3, title="T3 Filter") plot(T3FiboLine and T32 ? T32 : na, color=color2, linewidth=2, title="T3fibo") plot(showsupport ? MAvg : na, color=#0585E1, linewidth=2, title="Moving Avg Line") pALL=plot(PMax, color=color.red, linewidth=2, title="PMax", transp=100)

buySignalk = crossover(MAvg, PMax)

plotshape(buySignalk and showsignalsk ? PMax*0.995 : na, title="Buy", text="買/売ポジ閉じ", location=location.absolute, style=shape.labelup, size=size.tiny, color=color.green, textcolor=color.white, transp=10)

sellSignallk = crossunder(MAvg, PMax) plotshape(sellSignallk and showsignalsk ? PMax*1.005 : na, title="Sell", text="売/買ポジ閉じ", location=location.absolute, style=shape.labeldown, size=size.tiny, color=color.red, textcolor=color.white, transp=10) buySignalc = crossover(src, PMax) plotshape(buySignalc and showsignalsc ? PMax*0.995 : na, title="Buy-Price", text="C_BUY", location=location.absolute, style=shape.labelup, size=size.tiny, color=#0F18BF, textcolor=color.white, transp=0) sellSignallc = crossunder(src, PMax) plotshape(sellSignallc and showsignalsc ? PMax*1.005 : na, title="Sell-Price", text="C_SELL", location=location.absolute, style=shape.labeldown, size=size.tiny, color=#0F18BF, textcolor=color.white, transp=0) mPlot = plot(ohlc4, title="", style=plot.style_circles, linewidth=0,display=display.none) longFillColor = highlighting ? (MAvg>PMax ? color.green : na) : na shortFillColor = highlighting ? (MAvg<PMax ? color.red : na) : na fill(mPlot, pALL, title="Up Trend Cloud", color=longFillColor) fill(mPlot, pALL, title="Down Trend Cloud", color=shortFillColor)

tplevel = 0 //tplevel := tp1 ? nz(tplevel[1])==0 ? 1 : nz(tplevel[1])==1 ? 2 : 0 : nz(tplevel[1])==0 ? 0 : nz(tplevel[1])==1 ? 1 : nz(tplevel[1])==2 ? 2 : sellSignallk ? 0 : 0 //tplevel := sellSignallk or MAvg < PMax ? 0 : tp1 and nz(tplevel[1])==8 ? 9 : tp1 and nz(tplevel[1])==7 ? 8 : tp1 and nz(tplevel[1])==6 ? 7 : tp1 and nz(tplevel[1])==5 ? 6 : tp1 and nz(tplevel[1])==4 ? 5 : tp1 and nz(tplevel[1])==3 ? 4 : tp1 and nz(tplevel[1])==2 ? 3 : tp1 and nz(tplevel[1])==1 ? 2 : nz(tplevel[1])==1 ? 1 : nz(tplevel[1])==2 ? 2 : nz(tplevel[1])==3 ? 3 : nz(tplevel[1])==4 ? 4 : nz(tplevel[1])==5 ? 5 : nz(tplevel[1])==6 ? 6 : nz(tplevel[1])==7 ? 7 : nz(tplevel[1])==8 ? 8 : nz(tplevel[1])==9 ? 9 : 1 tplevel := sellSignallk or MAvg < PMax ? 0 : Trail1 < Trail2 ? 0 : tp1 and nz(tplevel[1])==1 ? 2 : nz(tplevel[1])==1 ? 1 : nz(tplevel[1])==2 ? 2 : 1

exitlevel = 0

exitlevel := sellSignallk or MAvg < PMax ? 0 : Sell and nz(tplevel[1])==2 and nz(exitlevel[1])==1 ? 2 : Sell and nz(tplevel[1])==2 and nz(exitlevel[1])==2 ? 3 : Sell and nz(tplevel[1])==2 and nz(exitlevel[1])==3 ? 4 : Sell and nz(tplevel[1])==2 and nz(exitlevel[1])==4 ? 5: nz(exitlevel[1])==1 ? 1 : nz(exitlevel[1])==2 ? 2 : nz(exitlevel[1])==3 ? 3 : nz(exitlevel[1])==4 ? 4 : nz(exitlevel[1])==5 ? 5: 1

plotchar(tplevel==0 and tplevelshow, char='0', color=color.green) plotchar(tplevel==1 and tplevelshow , char='1', color=color.green) plotchar(tplevel==2 and tplevelshow, char='2', color=color.green)

plotshape(exitlevel==0 and tplevelshow , text='0', location=location.belowbar, style=shape.triangledown, color=color.red) plotshape(exitlevel==1 and tplevelshow , text='1', location=location.belowbar, style=shape.triangledown, color=color.red) plotshape(exitlevel==2 and tplevelshow , text='2', location=location.belowbar, style=shape.triangledown, color=color.red) plotshape(exitlevel==3 and tplevelshow , text='3', location=location.belowbar, style=shape.triangledown, color=color.red) plotshape(exitlevel==4 and tplevelshow , text='4', location=location.belowbar, style=shape.triangledown, color=color.red) plotshape(exitlevel==5 and tplevelshow , text='5', location=location.belowbar, style=shape.triangledown, color=color.red)

plotshape(nz(tplevel[1])==2 and Sell and exitlevel>=2, title="TP", text="TP", location=location.abovebar, style=shape.labeldown, size=size.tiny, color=color.lime, textcolor=color.white,transp=0)

/// PERIOD /// //testStartYear = input(2019, "Backtest Start Year") //testStartMonth = input(1, "Backtest Start Month") //testStartDay = input(1, "Backtest Start Day") //testPeriodStart = timestamp(testStartYear,testStartMonth,testStartDay,0,0) // //testStopYear = input(2020, "Backtest Stop Year") //testStopMonth = input(12, "Backtest Stop Month") //testStopDay = input(31, "Backtest Stop Day") //testPeriodStop = timestamp(testStopYear,testStopMonth,testStopDay,0,0) // //testPeriod() => // time >= testPeriodStart and time <= testPeriodStop ? true : false // //if testPeriod() //strategy.entry() //strategy.close()

if (buySignalk) strategy.entry("Buy", strategy.long, comment="")

if nz(tplevel[1])==2 and Sell and exitlevel==2 strategy.exit ("Exit1", from_entry="Buy", limit=close, qty_percent = 25, comment="利食い25％")

if nz(tplevel[1])==3 and Sell and exitlevel==3 strategy.exit ("Exit2", from_entry="Buy", limit=close, qty_percent = 33.3, comment="利食い33.3％")

if nz(tplevel[1])==4 and Sell and exitlevel==3 strategy.exit ("Exit3", from_entry="Buy", limit=close, qty_percent = 50, comment="利食い50％")

if nz(tplevel[1])==5 and Sell and exitlevel==3 strategy.exit ("Exit4", from_entry="Buy", limit=close, comment="利食い")

if (sellSignallk) strategy.close_all(comment = "")

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amar-i-lla13 · 8 years ago

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Enciende un cigarrillo en homenaje al fuego que no fuimos.

Avg2🌻

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chitwan1-blog · 5 years ago

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week 3 assignment

I have selected the Gap Minder code book. I have used python to perform frequency analysis. The three variables used are alcohol consumption, employee rate and armed force rate.

#Importing modules import pandas import numpy

data = pandas. read_csv(‘gapminder.csv’, low_memory = False)

#setting variables you will be working with to numeric data[‘alcconsumption’] = data[‘alcconsumption’].convert_objects(convert_numeric=True) data[‘armedforcesrate’] = data[‘armedforcesrate’].convert_objects(convert_numeric=True) data[’employrate’] = data[’employrate’].convert_objects(convert_numeric=True)

print (’employrate – 4 categories – quartiles’ ) data[’employq’]=pandas. Cut(data[’employrate’], 4, labels=[“1st Q”,”2nd Q”,”3rd Q”,”4th Q”]) c4 = data[’employq’].value_counts(sort=False, dropna=True) print(c4)

c7 = data[’employq’].value_counts(sort=False, normalize=True) print(c7)

#Creating categories for the new variables based on min, max, and mean values avg1 = data[‘alcconsumption’].mean(sort=False) min1 = data[‘alcconsumption’].min(sort=False) max1 = data[‘alcconsumption’].max(sort=False)

avg2 = data[‘armedforcesrate’].mean(sort=False) min2 = data[‘armedforcesrate’].min(sort=False) max2 = data[‘armedforcesrate’].max(sort=False) data[‘alclevel’] = pandas.cut(data[‘alcconsumption’], [min1 , avg1 , 15, max1]) c5 = data[‘alclevel’].value_counts(sort=False, dropna=True) print(c5) data[‘armlevel’] = pandas.cut(data[‘armedforcesrate’], [min2, avg2, 5.02, max2]) c6 = data[‘armlevel’].value_counts(sort=False, dropna=True) print(c6)

#printing frequency and percentages p1 = data[‘alclevel’].value counts(sort=False, normalize=True) print(‘Percentages for alclevel:’ , p1)

c1 = data[‘alclevel’].value counts(sort=False) print(‘Counts for alclevel:’, c1)

p2 = data[‘arm level’].value counts(sort=False, normalize=True) print(‘Percentages for arm level:’ , p2)

c2 = data[‘arm level’].value counts(sort=False) print(‘Counts for arm level:’, c2)

OUTPUT

1) Alcohol consumption

Alcohol consumption is categorised into 3 levels . Majority of the values for consumption of alcohol fall below average which accounts to 48.4 percent . 5.16 percent of values fall under the category of high consumption of alcohol .On an average it turns out be more than 15 L per person .Several countries such as Bermuda ,Netherlands ,Korea etc have their data missing , hence they are excluded from the frequency analysis .

2) Employee rate

Employee rate is divided into 4 categories .21.1 percent of values fall under the high employment range (75-100 percent ) and 21.1 percent of values fall under the low employment range of (0-25 percent ).An equal proportion of share of values fall neither under high nor low employment range .12 countries have their data missing hence they are excluded .

3) Armed Force Rate

Armed force rate is categorized into 3 levels .Majority of the values of armed force rate fall below average that stands around 1.44 percent of a country’s population.4.69 percent of total values fall under high armed force rate category which accounts to more than 5.2 percent of a country’s population .The higher we go above average smaller the frequency gets .Countries like Greenland ,Taiwan and Bermuda have their data missing hence they have been excluded .

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