︠dc8f8424-7b27-46df-b997-dd6a43bd405fs︠
%r
pnorm(260.5, mean=272, sd=9)
qnorm(0.10, mean=272, sd=9)
︡fb378f75-99ba-48e7-8326-af1d2e786353︡{"html":"0.100663895991501"}︡{"html":"260.466035910099"}︡{"done":true}︡
︠de1158fa-5295-4d5d-be4e-1758730df9c9︠
%r

x<-c(83, 51, 87, 60, 28, 95, 8, 27,
15, 10, 18, 16, 29, 54, 91, 8,
17, 55, 10, 35, 47, 77, 36, 17,
21, 36, 18, 40, 10, 7, 34, 27,
28, 56, 8, 25, 68, 146, 89, 18,
73, 69, 9, 37, 10, 82, 29, 8,
60, 61, 61, 18, 169, 25, 8, 26,
11, 83, 11, 42, 17, 14, 9, 12)

#print(x)
hist(x,nclass=7)

qt = quantile(x)
print(qt)
sprintf("Q1 = %2.2f",qt[1])

IQR = qt[4]-qt[2]
sprintf("IQR = %2.2f", IQR)
Q1 = qt[2]; Q3 = qt[4];
sprintf("1.5*IQR = %2.2f", 1.5*IQR)
out_rg1 = Q1-1.5*IQR
out_rg2 = Q3+1.5*IQR

sprintf("Q1-1.5*IQR = %2.2f", out_rg1)
sprintf("Q3+1.5*IQR = %2.2f", out_rg2)

print(x<out_rg2) # true if not outlier, false if outlier
x_out = (x<out_rg2)
xp = x[x_out]
print(xp)
sprintf("number of x > out_rg2 = %2.2f", sum(x>out_rg2))
sprintf("number of xp > out_rg2 = %2.2f", sum(xp>out_rg2))

xp1 = x[x<out_rg1]
xp2 = x[x>out_rg2]

print(xp1) #outliers below 1.5*Q1
print(xp2) #outliers above 1.5*Q3

qqnorm(x)
︡784c0864-10b1-467c-b353-88c1d806135c︡{"stdout":"    0%    25%    50%    75%   100% \n  7.00  14.75  28.00  60.00 169.00 \n"}︡{"html":"'Q1 = 7.00'"}︡{"html":"'IQR = 45.25'"}︡{"html":"'1.5*IQR = 67.88'"}︡{"html":"'Q1-1.5*IQR = -53.12'"}︡{"html":"'Q3+1.5*IQR = 127.88'"}︡{"stdout":" [1]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE\n[13]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE\n[25]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE\n[37]  TRUE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE\n[49]  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE\n[61]  TRUE  TRUE  TRUE  TRUE\n"}︡{"stdout":" [1] 83 51 87 60 28 95  8 27 15 10 18 16 29 54 91  8 17 55 10 35 47 77 36 17 21\n[26] 36 18 40 10  7 34 27 28 56  8 25 68 89 18 73 69  9 37 10 82 29  8 60 61 61\n[51] 18 25  8 26 11 83 11 42 17 14  9 12\n"}︡{"html":"'number of x &gt; out_rg2 = 2.00'"}︡{"html":"'number of xp &gt; out_rg2 = 0.00'"}︡{"stdout":"numeric(0)\n"}︡{"stdout":"[1] 146 169\n"}︡{"file":{"filename":"/tmp/tmpxdt1l_.png","show":false,"text":null,"uuid":"b194c4a4-de37-4e6d-a85a-244d1c051c4f"},"once":false}︡{"html":"<img src=\"/blobs//tmp/tmpxdt1l_.png?uuid=b194c4a4-de37-4e6d-a85a-244d1c051c4f\" smc-image-scaling=\"0.5\" />"}︡{"file":{"filename":"/tmp/tmpZ2Wq0J.png","show":false,"text":null,"uuid":"557df518-f0c6-4148-ab4f-fb7dfda1b708"},"once":false}︡{"html":"<img src=\"/blobs//tmp/tmpZ2Wq0J.png?uuid=557df518-f0c6-4148-ab4f-fb7dfda1b708\" smc-image-scaling=\"0.5\" />"}︡{"done":true}︡
︠1da7d3ec-8d12-4ce7-9200-5a0748e54e9cs︠
%r
x<-c(78, 92, 96, 100, 67, 105, 109, 75, 127, 111,
93, 114, 82, 100, 125, 67, 94, 74, 81, 98,
102, 108, 81, 96, 103, 91, 90, 96, 86, 92,
84, 92, 90, 103, 115, 93, 85, 116, 87, 106,
85, 88, 106, 104, 102, 98, 116, 107, 102, 89)

hist(x, nclass = 7)

qt = quantile(x)
print(qt)

IQR = qt[4]-qt[2]
sprintf("IQR = %2.2f", IQR)
Q1 = qt[2]; Q3 = qt[4];
sprintf("1.5*IQR = %2.2f", 1.5*IQR)
out_rg1 = Q1-1.5*IQR
out_rg2 = Q3+1.5*IQR

sprintf("Q1-1.5*IQR = %2.2f", out_rg1)
sprintf("Q3+1.5*IQR = %2.2f", out_rg2)

#print(x<out_rg2)
x_out = (x<out_rg2)
xp = x[x_out]
#print(xp)
sprintf("number of x > out_rg2 = %2.2f", sum(x>out_rg2))
sprintf("number of xp > out_rg2 = %2.2f", sum(xp>out_rg2))
xp1 = x[x<out_rg1]
xp2 = x[x>out_rg2]

print(xp1) #outliers below 1.5*Q1
print(xp2) #outliers above 1.5*Q3

qqnorm(x)
︡80a87e21-da9e-49e9-a874-827a53493fe6︡{"stdout":"    0%    25%    50%    75%   100% \n 67.00  87.25  96.00 104.75 127.00 \n"}︡{"html":"'IQR = 17.50'"}︡{"html":"'1.5*IQR = 26.25'"}︡{"html":"'Q1-1.5*IQR = 61.00'"}︡{"html":"'Q3+1.5*IQR = 131.00'"}︡{"html":"'number of x &gt; out_rg2 = 0.00'"}︡{"html":"'number of xp &gt; out_rg2 = 0.00'"}︡{"stdout":"numeric(0)\n"}︡{"stdout":"numeric(0)\n"}︡{"file":{"filename":"/tmp/tmpA8ZKAE.png","show":false,"text":null,"uuid":"a7803d84-26c3-4118-82b3-35f0a74cd916"},"once":false}︡{"html":"<img src=\"/blobs//tmp/tmpA8ZKAE.png?uuid=a7803d84-26c3-4118-82b3-35f0a74cd916\" smc-image-scaling=\"0.5\" />"}︡{"file":{"filename":"/tmp/tmpSiDTkD.png","show":false,"text":null,"uuid":"9d71de7f-c9a4-48bc-8099-371360356e3e"},"once":false}︡{"html":"<img src=\"/blobs//tmp/tmpSiDTkD.png?uuid=9d71de7f-c9a4-48bc-8099-371360356e3e\" smc-image-scaling=\"0.5\" />"}︡{"done":true}︡
︠5ec81cf1-86e4-4160-b6f7-b0c0c0c9a6f0s︠
%r

#n=10;
#x<-sample(c(0,1), replace=TRUE, size=n)
#print(x)

n=500
N = 500
X <-c()
for (i in seq(1,N)){
    X[i]<-mean(sample(c(0,1), replace=TRUE, size=n))
}

print(X)
hist(X)
︡ecf83ace-7f96-4a36-9e56-866d9df4e17f︡{"stdout":"  [1] 0.532 0.472 0.520 0.474 0.478 0.500 0.498 0.514 0.520 0.492 0.510 0.496\n [13] 0.478 0.486 0.504 0.554 0.528 0.520 0.532 0.498 0.494 0.508 0.534 0.508\n [25] 0.504 0.462 0.490 0.516 0.518 0.478 0.476 0.484 0.490 0.528 0.486 0.506\n [37] 0.492 0.470 0.502 0.492 0.516 0.490 0.528 0.538 0.462 0.494 0.526 0.508\n [49] 0.502 0.492 0.464 0.476 0.506 0.506 0.526 0.492 0.474 0.518 0.474 0.524\n [61] 0.448 0.450 0.518 0.524 0.490 0.488 0.490 0.496 0.484 0.442 0.484 0.530\n [73] 0.494 0.534 0.484 0.492 0.524 0.528 0.542 0.498 0.474 0.548 0.482 0.504\n [85] 0.500 0.472 0.480 0.550 0.498 0.476 0.518 0.496 0.472 0.524 0.514 0.472\n [97] 0.482 0.422 0.500 0.520 0.484 0.532 0.446 0.496 0.484 0.512 0.532 0.500\n[109] 0.530 0.514 0.466 0.520 0.590 0.496 0.512 0.516 0.488 0.488 0.464 0.502\n[121] 0.494 0.518 0.514 0.510 0.538 0.506 0.510 0.468 0.514 0.492 0.476 0.496\n[133] 0.512 0.524 0.516 0.498 0.514 0.490 0.526 0.508 0.504 0.526 0.514 0.516\n[145] 0.516 0.482 0.506 0.462 0.518 0.480 0.524 0.520 0.520 0.476 0.500 0.466\n[157] 0.468 0.482 0.478 0.556 0.512 0.466 0.528 0.478 0.498 0.486 0.506 0.498\n[169] 0.522 0.540 0.538 0.520 0.542 0.518 0.454 0.514 0.512 0.492 0.528 0.494\n[181] 0.522 0.498 0.524 0.494 0.466 0.472 0.532 0.522 0.510 0.462 0.492 0.508\n[193] 0.496 0.514 0.504 0.484 0.492 0.506 0.532 0.530 0.490 0.456 0.516 0.508\n[205] 0.508 0.532 0.472 0.494 0.496 0.528 0.486 0.482 0.528 0.480 0.518 0.468\n[217] 0.532 0.536 0.486 0.488 0.474 0.516 0.516 0.500 0.520 0.510 0.484 0.508\n[229] 0.518 0.506 0.484 0.492 0.484 0.534 0.546 0.486 0.462 0.488 0.504 0.482\n[241] 0.534 0.462 0.518 0.512 0.496 0.522 0.516 0.472 0.490 0.496 0.498 0.486\n[253] 0.496 0.454 0.500 0.482 0.512 0.498 0.542 0.500 0.552 0.492 0.474 0.490\n[265] 0.526 0.488 0.480 0.546 0.478 0.506 0.520 0.496 0.508 0.472 0.470 0.504\n[277] 0.518 0.528 0.496 0.500 0.450 0.502 0.476 0.498 0.498 0.492 0.484 0.524\n[289] 0.508 0.496 0.470 0.474 0.444 0.456 0.504 0.498 0.522 0.464 0.484 0.500\n[301] 0.526 0.524 0.494 0.510 0.534 0.514 0.478 0.486 0.466 0.484 0.492 0.522\n[313] 0.502 0.506 0.518 0.490 0.506 0.480 0.512 0.470 0.522 0.500 0.470 0.514\n[325] 0.518 0.508 0.518 0.516 0.492 0.530 0.530 0.494 0.496 0.494 0.476 0.508\n[337] 0.490 0.544 0.490 0.472 0.514 0.490 0.504 0.528 0.502 0.528 0.528 0.488\n[349] 0.526 0.502 0.486 0.524 0.480 0.524 0.498 0.488 0.470 0.468 0.514 0.462\n[361] 0.524 0.514 0.516 0.502 0.474 0.532 0.506 0.480 0.498 0.492 0.478 0.512\n[373] 0.556 0.498 0.480 0.488 0.500 0.510 0.486 0.496 0.484 0.480 0.522 0.508\n[385] 0.490 0.548 0.498 0.514 0.478 0.524 0.460 0.512 0.504 0.464 0.526 0.492\n[397] 0.458 0.478 0.512 0.514 0.488 0.510 0.506 0.502 0.494 0.480 0.504 0.486\n[409] 0.478 0.440 0.536 0.512 0.514 0.510 0.478 0.504 0.500 0.490 0.464 0.488\n[421] 0.488 0.494 0.500 0.532 0.512 0.492 0.500 0.520 0.502 0.484 0.510 0.476\n[433] 0.484 0.494 0.496 0.504 0.494 0.546 0.498 0.548 0.506 0.488 0.458 0.498\n[445] 0.510 0.558 0.496 0.528 0.484 0.490 0.504 0.462 0.508 0.496 0.508 0.480\n[457] 0.514 0.494 0.518 0.532 0.522 0.472 0.538 0.484 0.498 0.534 0.514 0.494\n[469] 0.460 0.484 0.482 0.504 0.482 0.490 0.524 0.514 0.496 0.488 0.504 0.528\n[481] 0.502 0.474 0.502 0.524 0.522 0.520 0.480 0.510 0.476 0.522 0.502 0.484\n[493] 0.498 0.522 0.508 0.520 0.498 0.530 0.474 0.502\n"}︡{"file":{"filename":"/tmp/tmp7100fq.png","show":false,"text":null,"uuid":"9b6d0e65-ae6b-47f3-b01d-f2d9b50afc97"},"once":false}︡{"html":"<img src=\"/blobs//tmp/tmp7100fq.png?uuid=9b6d0e65-ae6b-47f3-b01d-f2d9b50afc97\" smc-image-scaling=\"0.5\" />"}︡{"done":true}︡
︠06bcbb96-e8c2-4e11-a5e6-f671982f3175s︠


%r

# calc P(x>84) for normal distr'n mean 72 sd = 15.2
#pnorm(84, mean=72, sd=15.2, lower.tail=FALSE)


# The length of a human pregnancy is normally distributed with a mean of 272 days
# with a standard deviation of 9 days
# find P(x>280)
#pnorm(280, mean=272, sd=9, lower.tail = FALSE)

data <- rnorm(500, mean=0, sd=1) # generate random data sampled from normal dist
hist(data,freq = FALSE, col="red") #histogram the data
x<-seq(-4,+4,by=0.02) #create sequence of x-vales around data mean for plotting

curve(dnorm(x, mean=0, sd=1), add=TRUE, col="black", lwd=2)
#plot data values. dnorm returns height at a given input value of the pdf
︡114d98d1-0808-4659-8894-556419c4315e︡{"file":{"filename":"/tmp/tmpNd6sJO.png","show":false,"text":null,"uuid":"1e86203c-dee1-44ea-90c0-2ee51d3473e8"},"once":false}︡{"html":"<img src=\"/blobs//tmp/tmpNd6sJO.png?uuid=1e86203c-dee1-44ea-90c0-2ee51d3473e8\" smc-image-scaling=\"0.5\" />"}︡{"done":true}︡