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[1]
sprintf("1.5*IQR = %2.2f", 1.5*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)

num_out1 = sum((x<out_rg1))
num_out2 = sum((x>out_rg2))
sprintf("number of x > Q3+1.5*IQR = %2.2f",
        num_out2)
sprintf("number of x < Q1-1.5*IQR = %2.2f",
        num_out1)
x_out1 = x[x<Q1-1.5*IQR]
x_out2 = x[x>Q3+1.5*IQR]

print("outliers below Q1-1.5*IQR = ")
print(x_out1)
print("outliers above Q3+1.5*IQR = ")
print(x_out2)
qqnorm(x)