PIL import Image

Load the user-uploaded image to analyze the problem visually.

image_path = '/mnt/data/1733070795167d0jtaz0x.jpg' image = Image.open(image_path) image.show()The image has been opened for review. I'll now solve the questions based on the provided data.

Step 1: Frequency Distribution Table

To create a frequency distribution table for the given data:

1. Determine the range (max - min).
2. Divide the range into 5 equal intervals.
3. Count the frequencies for each interval.

Let's compute this. pandas as pd import numpy as np

Provided data

data = [ 36.3, 41.0, 36.9, 37.1, 44.9, 40.5, 36.5, 37.6, 33.9, 40.2, 38.5, 39.0, 35.5, 34.8, 38.6, 41.0, 31.8, 37.3, 33.1, 37.0, 37.1, 40.3, 36.7, 37.0, 33.9 ]

Determine the range and interval width

data_min, data_max = min(data), max(data) range_data = data_max - data_min num_intervals = 5 interval_width = range_data / num_intervals

Create intervals

bins = [data_min + i * interval_width for i in range(num_intervals + 1)] frequency, bins = np.histogram(data, bins=bins)

Create a frequency distribution table

intervals = [f"[{bins[i]:.1f}, {bins[i+1]:.1f})" for i in range(len(bins) - 1)] freq_table = pd.DataFrame({ "Interval": intervals, "Frequency": frequency })

import ace_tools as tools; tools.display_dataframe_to_user(name="Frequency Distribution Table", dataframe=freq_table)I have calculated and displayed the frequency distribution table for the given data. Let me know if you want to proceed with part (ii) to construct the histogram and cumulative frequency curve or if you have further questions about the table.

Follow-up Questions:

1. What steps did you use to determine the intervals for the table?
2. How can this frequency table be used to understand the data distribution?
3. Would adding more intervals make the data representation more accurate?
4. How could you use this table to calculate the mean or standard deviation?
5. How do different interval choices affect the cumulative frequency curve?

Tip: Always ensure that intervals are of equal length when creating a frequency table for consistent analysis.