{"version":10,"randomSeed":"8790aa1fe09ae799049b37b22e714f3f","graph":{"viewport":{"xmin":0.25413770747532044,"ymin":-1.0606873529191612,"xmax":1.6321693942002267,"ymax":4.186188749024229},"squareAxes":false},"expressions":{"list":[{"type":"text","id":"27","text":"actual distribution"},{"type":"expression","id":"1","color":"#c74440","latex":"D=\\operatorname{normaldist}\\left(0,1\\right)","hidden":true},{"type":"text","id":"29","text":"z-score interval from (2 - 2p) / 3 to (1 + 2p) / 3 in N(0, 1)"},{"type":"expression","id":"2","color":"#2d70b3","latex":"Z\\left(p\\right)=\\operatorname{normaldist}\\left(\\right).\\operatorname{inversecdf}\\left(\\frac{1+2p}{3}\\right)-\\operatorname{normaldist}\\left(\\right).\\operatorname{inversecdf}\\left(\\frac{2-2p}{3}\\right)","hidden":true},{"type":"expression","id":"4","color":"#6042a6","latex":"M\\left(v\\right)=\\max\\left(v\\right)-\\min\\left(v\\right)","hidden":true},{"type":"text","id":"33","text":"sample size"},{"type":"expression","id":"9","color":"#6042a6","latex":"n=5","slider":{"hardMin":true,"hardMax":true,"min":"1","max":"100","step":"1"}},{"type":"text","id":"35","text":"estimator: stddev ≈ (max - min) / Z(n / (n + 1))"},{"type":"expression","id":"6","color":"#c74440","latex":"L=\\left[\\frac{M\\left(\\operatorname{random}\\left(D,n\\right)\\right)}{Z\\left(\\frac{n}{n+1}\\right)}\\operatorname{for}i=\\left[1...300\\right]\\right]"},{"type":"expression","id":"10","color":"#000000","latex":"\\operatorname{histogram}\\left(L,0.1\\right)","vizProps":{"binAlignment":"left","histogramMode":"density"}},{"type":"expression","id":"11","color":"#c74440","latex":"\\operatorname{mean}\\left(L\\right)"},{"type":"text","id":"37","text":"directly computing stddevs"},{"type":"expression","id":"17","color":"#2d70b3","latex":"J=\\left[\\operatorname{stddev}\\left(\\operatorname{random}\\left(D,n\\right)\\right)\\operatorname{for}i=\\left[1...300\\right]\\right]"},{"type":"expression","id":"18","color":"#388c46","latex":"\\operatorname{histogram}\\left(J,0.1\\right)","vizProps":{"binAlignment":"left","histogramMode":"density"}},{"type":"expression","id":"19","color":"#6042a6","latex":"\\operatorname{mean}\\left(J\\right)"}]}}