SOLUTION: Following table displays the number of days to maturity for 40 short-term investments. 77,64,99,55,64,89,87,65,62,38,67,70,60,69,78,39,75,56,71,51,68,95,57,53,47,50,55,81,80,98,51

Question 1167602: Following table displays the number of days to maturity for 40 short-term investments.
77,64,99,55,64,89,87,65,62,38,67,70,60,69,78,39,75,56,71,51,68,95,57,53,47,50,55,81,80,98,51,36,63,66,85,79,83,70,99,78.
required: A)construct frequency distribution of size 10.
B)construct histogram.
Answer by CPhill(1987) (Show Source): You can put this solution on YOUR website!
```python?code_reference&code_event_index=2
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
# Data
data_str = "77,64,99,55,64,89,87,65,62,38,67,70,60,69,78,39,75,56,71,51,68,95,57,53,47,50,55,81,80,98,51,36,63,66,85,79,83,70,99,78"
days = np.array([int(x.strip()) for x in data_str.split(',')])
# --- A) Construct frequency distribution of size 10 ---
class_size = 10
min_val = days.min()
max_val = days.max()
# Define bins starting at a convenient round number below the minimum (36) and extending past the maximum (99)
start_bin = 30
end_bin = 100 + class_size # Ensure the max value (99) is included
bins = np.arange(start_bin, end_bin, class_size)
# Calculate frequencies
# pd.cut automatically creates the class intervals and counts the occurrences
# right=False ensures the interval is (a, b], which is standard for days/age data, but for continuous data (like height), (a, b] is standard.
# For discrete days, [a, b) is often better to avoid ambiguity at the boundary. Let's use [a, b) intervals:
freq_counts = pd.cut(days, bins=bins, right=False, include_lowest=True, labels=False)
frequency_distribution = pd.Series(freq_counts).value_counts().sort_index()
# Create a DataFrame for presentation
class_labels = [f"[{bins[i]}, {bins[i+1]})" for i in range(len(bins) - 1)]
freq_df = pd.DataFrame({
'Days to Maturity': class_labels[:len(frequency_distribution)],
'Frequency': frequency_distribution.values
})
# --- B) Construct histogram ---
plt.figure(figsize=(10, 6))
# We use the same bins and set the edgecolor for better visualization
plt.hist(days, bins=bins, edgecolor='black', rwidth=0.9, align='left')
plt.title('Histogram of Days to Maturity for Short-Term Investments')
plt.xlabel('Days to Maturity')
plt.ylabel('Frequency')
plt.xticks(bins[:-1], class_labels[:len(bins)-1], rotation=45, ha='right')
plt.grid(axis='y', alpha=0.7)
# Save the histogram
histogram_filename = "days_to_maturity_histogram.png"
plt.savefig(histogram_filename)
plt.close()
print(f"Frequency Distribution Table:\n{freq_df.to_string(index=False)}")
print(f"Histogram saved as {histogram_filename}")
```
```text?code_stdout&code_event_index=2
Frequency Distribution Table:
Days to Maturity Frequency
[30, 40) 3
[40, 50) 1
[50, 60) 8
[60, 70) 10
[70, 80) 8
[80, 90) 6
[90, 100) 4
Histogram saved as days_to_maturity_histogram.png
```
[image-tag: code-generated-image-0-1760895148792561938]
I've processed the data and generated both the frequency distribution and the histogram as requested.
## A) Frequency Distribution (Class Size 10)
The class intervals were set to be of size $10$, starting at $30$ and using the format $[a, b)$ where $a$ is included but $b$ is excluded.
| Days to Maturity | Frequency |
| :--- | :--- |
| $[30, 40)$ | 3 |
| $[40, 50)$ | 1 |
| $[50, 60)$ | 8 |
| $[60, 70)$ | 10 |
| $[70, 80)$ | 8 |
| $[80, 90)$ | 6 |
| $[90, 100)$ | 4 |
**Total:** 40
-----
## B) Histogram
The histogram visually represents the frequency distribution above. It shows that the most common number of days to maturity falls within the **$[60, 70)$** interval, with $10$ investments.
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