import math

X = [12,37,45,39,38,29,14,23,39,34,12,28,41,38,24,25,27,
     39,43,25,24,41,49,40,40,23,26,34,17,36,38,36,39,56,
     38,19,36,30,35,30,22,29,33,28,38,49,40,45,21,45,32,
     34,12,37,23,33,12,26,41,35,47,22,48,35,15,35,28,20,
     31,35,32,40,27,34,15,40,39,27,41,21,48,27,32,35,32,
     41,40,28,38,49,24,33,26,27,47,16,57,25,24,32]

Y = [42,23,7,35,20,25,36,44,24,13,34,29,48,32,44,35,37,
     13,17,18,40,21,24,24,35,45,42,37,33,35,24,29,15,19,
     35,40,16,30,24,34,32,31,24,39,19,24,32,27,30,17,41,
     39,39,28,39,25,33,37,40,31,30,35,34,27,34,18,30,32,
     23,26,28,27,33,15,32,18,15,31,35,35,24,22,14,34,25,
     8,31,30,10,23,38,22,31,29,25,27,31,44,42,41]
print('===============Number 1===============')

xMax = max(X)
xMin = min(X)
n = len(X)

print('n =', n)
print('xMax =', xMax)
print('xMin =', xMin)

h=(xMax - xMin) / (1 + 3.322*math.log10(n))
print('h =', h, ' or ', round(h, 1))
h = round(h, 1)

leftEndConst = round((xMin - (h/2)),2)

print('leftEnd =', leftEndConst)

nI = 0
sumNi = 0
print('============TABLICA 4ASTOT============')
leftEnd = leftEndConst
wIdivHarray = []
intervalsArray = []
print('line             ', 'nI  ', 'wI  ', 'wI/h')
while sumNi != n:
    rightEnd = round((leftEnd + h), 2)
    for i in X:
        if (i > leftEnd) and (i <= rightEnd):
            nI=nI+1;
    wI = round((nI/n),2)
    wIdivH = round((wI / h),3)
    wIdivHarray.append(wIdivH)
    intervalsArray.append('('+str(leftEnd)+';'+str(rightEnd)+']')
    print('(',leftEnd,';',rightEnd,']', '|', nI, '|', wI, '|', wIdivH)
    sumNi = sumNi + nI
    nI = 0
    leftEnd = rightEnd
print('======================================')
print('===============Number 2===============')
print('x:intervals  y:wI/h')
intervalsArray[len(intervalsArray)-1] = ('('+str(leftEnd - h)+';'+str(xMax)+']')

for i in range(len(wIdivHarray)):
    print(intervalsArray[i], wIdivHarray[i])
print('======================================')
print('===============Number 3===============')

notX = round((sum(X)/n), 3)
notY = round((sum(Y)/n), 3)

print('X^ =', notX)
print('Y^ =', notY)

sqrX = X
for i in range(len(sqrX)):
    sqrX[i] = sqrX[i] * sqrX[i]

sqrY = Y
for i in range(len(sqrY)):
    sqrY[i] = sqrY[i] * sqrY[i]

print('S*2(X) =',round(((sum(sqrX) - n * notX * notX) / (n - 1)), 4))
print('S*2(Y) =',round(((sum(sqrY) - n * notY * notY) / (n - 1)), 4))

print('S*(X)', math.sqrt(round(((sum(sqrX) - n * notX * notX) / (n - 1)), 4)))
print('S*(Y)', math.sqrt(round(((sum(sqrY) - n * notY * notY) / (n - 1)), 4)))
print('======================================')