import matplotlib.pyplot as plt
intervals = [10, 20, 30, 40, 50, 60, 70, 80, 90]
frequencies = [4, 6, 8, 10, 12, 14, 7, 5]
midpoints = [(intervals[i] + intervals[i+1]) / 2 for i in range(len(frequencies))]
midpoints = [intervals[0]] + midpoints + [intervals[-1]]
frequencies = [0] + frequencies + [0]
plt.plot(midpoints, frequencies, marker='o', linestyle='-', color='r')
plt.xlabel('Intervals')
plt.ylabel('Frequencies')
plt.title('Frequency Polygon')
plt.grid(True)
plt.show()