import math

def calc(sample):
    minimum =min(sample)
    maximum=max(sample)
    print(minimum,maximum)
    ran = maximum-minimum

    n= len(sample)
    mean = sum(sample)/n
    sum1 = 0
    for i in range(n):
        sum1 = (sample[i]-mean)**2
    std_dev = math.sqrt(1/n*sum1)
    ratio = ran/std_dev if std_dev != 0 else 0
    
    return {'min': minimum, 'max': maximum, 'range': ran, 'deviation': std_dev,'range to stddev': ratio, 'samplesize': n}

def intervals(sample,m):
    stats =calc(sample)

    minimum = stats['min']
    maximum =stats['max']

    sortedsam = sorted(sample)
    n=len(sortedsam)

    width =(maximum-minimum)/m
    bounds = [minimum + i*width for i in range(m+1)]

    c = [0]*m
    s = 0

    for i in range(m):
        lower = bounds[i]
        upper = bounds[i+1]

        while s < n and sortedsam[s] <= upper:
            if i ==m-1:
                if sortedsam[s] >= lower:
                    c[i]+=1
            else:
                if lower <=sortedsam[s] < upper:
                    c[i]+=1
            s +=1

    return bounds, c