The image contains a question asking for the construction of a frequency polygon based on the given ACFP (Accumulated Cumulative Frequency Polygon). Let me extract and solve it for you.

Steps to Solve:

1. Interpret the ACFP (Cumulative Frequency Graph):

   • Identify cumulative frequencies from the graph at each class boundary.
   • Calculate the class frequencies by subtracting successive cumulative frequencies.

2. Prepare Frequency Data:

   • Use the class boundaries and the calculated frequencies to create the frequency table.

3. Draw the Frequency Polygon:

   • Use the midpoints of the class intervals on the x-axis.
   • Plot the frequencies against the midpoints and connect the points.

Let me extract the data and provide the solution. matplotlib.pyplot as plt

Class boundaries from the graph

class_boundaries = [-5, 0, 5, 10, 15, 20]

Cumulative frequencies from the graph (manually extracted)

cumulative_frequencies = [0, 5, 15, 30, 40, 50]

Calculate frequencies from cumulative frequencies

frequencies = [cumulative_frequencies[i] - cumulative_frequencies[i - 1] for i in range(1, len(cumulative_frequencies))]

Midpoints of class intervals

midpoints = [(class_boundaries[i] + class_boundaries[i + 1]) / 2 for i in range(len(class_boundaries) - 1)]

Plotting the frequency polygon

plt.figure(figsize=(8, 6)) plt.plot(midpoints, frequencies, marker='o', linestyle='-', color='b', label='Frequency Polygon') plt.title('Frequency Polygon') plt.xlabel('Class Midpoints') plt.ylabel('Frequency') plt.grid(True) plt.legend() plt.show()

Display the extracted data as a table

class_boundaries, cumulative_frequencies, frequencies### Results:

• Class Boundaries: [-5, 0, 5, 10, 15, 20]
• Cumulative Frequencies: [0, 5, 15, 30, 40, 50]
• Frequencies (calculated): [5, 10, 15, 10, 10]

The frequency polygon has been plotted using the midpoints of the class intervals and the corresponding frequencies.

Explanation:

1. Frequency Calculation: $f_i = CF_i - CF_{i-1}$ This gives the individual frequencies for each class interval.

2. Midpoints: These are calculated as the average of the two boundaries for each class, e.g., $(-5 + 0)/2 = -2.5$.

3. Polygon Construction: Frequencies are plotted against midpoints, and the points are connected with lines.

Would you like more details or a step-by-step breakdown of this process?

Related Questions:

1. What is the importance of using midpoints in a frequency polygon?
2. Can a frequency polygon be drawn using cumulative frequencies?
3. How do we interpret frequency polygons in terms of data distribution?
4. What other graphs can be derived from cumulative frequency data?
5. What are the advantages of frequency polygons over histograms?

Tip:

Always ensure that axes are properly labeled and scaled for clarity when plotting statistical graphs.