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def cumulative_frequencies(frequencies):
    cumulative = [frequencies[0]]
    for i in range(1, len(frequencies)):
        cumulative.append(cumulative[i-1] + frequencies[i])
    return cumulative

def quartile_deviation_grouped(data, frequencies):
    n = sum(frequencies)
    cf = cumulative_frequencies(frequencies)
    q1_index = (n + 1) / 4
    q3_index = 3 * (n + 1) / 4
    
    q1, q3 = None, None
    for i in range(len(cf)):
        if cf[i] >= q1_index and q1 is None:
            q1 = data[i] + ((q1_index - cf[i-1]) / frequencies[i]) * (data[i+1] - data[i])
        if cf[i] >= q3_index and q3 is None:
            q3 = data[i] + ((q3_index - cf[i-1]) / frequencies[i]) * (data[i+1] - data[i])
        if q1 is not None and q3 is not None:
            break
    
    quartile_deviation = (q3 - q1) / 2
    return quartile_deviation

data = [10, 20, 30, 40, 50]  # Class intervals
frequencies = [5, 8, 12, 10, 5]  # Frequencies of each class interval

result = quartile_deviation_grouped(data, frequencies)
print("Quartile deviation for grouped data:", result)