document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167602>Question 1167602</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Following table displays the number of days to maturity for 40 short-term investments.<BR>\n" );
document.write( "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.\r<BR>\n" );
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document.write( "required: A)construct frequency distribution of size 10.<BR>\n" );
document.write( "          B)construct histogram. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852320 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=852320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ```python?code_reference&code_event_index=2<BR>\n" );
document.write( "import pandas as pd<BR>\n" );
document.write( "import numpy as np<BR>\n" );
document.write( "import matplotlib.pyplot as plt\r<BR>\n" );
document.write( "\n" );
document.write( "# Data<BR>\n" );
document.write( "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\"<BR>\n" );
document.write( "days = np.array([int(x.strip()) for x in data_str.split(',')])\r<BR>\n" );
document.write( "\n" );
document.write( "# --- A) Construct frequency distribution of size 10 ---<BR>\n" );
document.write( "class_size = 10<BR>\n" );
document.write( "min_val = days.min()<BR>\n" );
document.write( "max_val = days.max()\r<BR>\n" );
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document.write( "# Define bins starting at a convenient round number below the minimum (36) and extending past the maximum (99)<BR>\n" );
document.write( "start_bin = 30<BR>\n" );
document.write( "end_bin = 100 + class_size  # Ensure the max value (99) is included<BR>\n" );
document.write( "bins = np.arange(start_bin, end_bin, class_size)\r<BR>\n" );
document.write( "\n" );
document.write( "# Calculate frequencies<BR>\n" );
document.write( "# pd.cut automatically creates the class intervals and counts the occurrences<BR>\n" );
document.write( "# 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.<BR>\n" );
document.write( "# For discrete days, [a, b) is often better to avoid ambiguity at the boundary. Let's use [a, b) intervals:<BR>\n" );
document.write( "freq_counts = pd.cut(days, bins=bins, right=False, include_lowest=True, labels=False)<BR>\n" );
document.write( "frequency_distribution = pd.Series(freq_counts).value_counts().sort_index()\r<BR>\n" );
document.write( "\n" );
document.write( "# Create a DataFrame for presentation<BR>\n" );
document.write( "class_labels = [f\"[{bins[i]}, {bins[i+1]})\" for i in range(len(bins) - 1)]<BR>\n" );
document.write( "freq_df = pd.DataFrame({<BR>\n" );
document.write( "    'Days to Maturity': class_labels[:len(frequency_distribution)],<BR>\n" );
document.write( "    'Frequency': frequency_distribution.values<BR>\n" );
document.write( "})\r<BR>\n" );
document.write( "\n" );
document.write( "# --- B) Construct histogram ---<BR>\n" );
document.write( "plt.figure(figsize=(10, 6))<BR>\n" );
document.write( "# We use the same bins and set the edgecolor for better visualization<BR>\n" );
document.write( "plt.hist(days, bins=bins, edgecolor='black', rwidth=0.9, align='left')\r<BR>\n" );
document.write( "\n" );
document.write( "plt.title('Histogram of Days to Maturity for Short-Term Investments')<BR>\n" );
document.write( "plt.xlabel('Days to Maturity')<BR>\n" );
document.write( "plt.ylabel('Frequency')<BR>\n" );
document.write( "plt.xticks(bins[:-1], class_labels[:len(bins)-1], rotation=45, ha='right')<BR>\n" );
document.write( "plt.grid(axis='y', alpha=0.7)\r<BR>\n" );
document.write( "\n" );
document.write( "# Save the histogram<BR>\n" );
document.write( "histogram_filename = \"days_to_maturity_histogram.png\"<BR>\n" );
document.write( "plt.savefig(histogram_filename)<BR>\n" );
document.write( "plt.close()\r<BR>\n" );
document.write( "\n" );
document.write( "print(f\"Frequency Distribution Table:\n{freq_df.to_string(index=False)}\")<BR>\n" );
document.write( "print(f\"Histogram saved as {histogram_filename}\")\r<BR>\n" );
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document.write( "```\r<BR>\n" );
document.write( "\n" );
document.write( "```text?code_stdout&code_event_index=2<BR>\n" );
document.write( "Frequency Distribution Table:<BR>\n" );
document.write( "Days to Maturity  Frequency<BR>\n" );
document.write( "        [30, 40)          3<BR>\n" );
document.write( "        [40, 50)          1<BR>\n" );
document.write( "        [50, 60)          8<BR>\n" );
document.write( "        [60, 70)         10<BR>\n" );
document.write( "        [70, 80)          8<BR>\n" );
document.write( "        [80, 90)          6<BR>\n" );
document.write( "       [90, 100)          4<BR>\n" );
document.write( "Histogram saved as days_to_maturity_histogram.png\r<BR>\n" );
document.write( "\n" );
document.write( "```\r<BR>\n" );
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document.write( "[image-tag: code-generated-image-0-1760895148792561938]\r<BR>\n" );
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document.write( "I've processed the data and generated both the frequency distribution and the histogram as requested.\r<BR>\n" );
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document.write( "## A) Frequency Distribution (Class Size 10)\r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "| Days to Maturity | Frequency |<BR>\n" );
document.write( "| :--- | :--- |<BR>\n" );
document.write( "| $[30, 40)$ | 3 |<BR>\n" );
document.write( "| $[40, 50)$ | 1 |<BR>\n" );
document.write( "| $[50, 60)$ | 8 |<BR>\n" );
document.write( "| $[60, 70)$ | 10 |<BR>\n" );
document.write( "| $[70, 80)$ | 8 |<BR>\n" );
document.write( "| $[80, 90)$ | 6 |<BR>\n" );
document.write( "| $[90, 100)$ | 4 |\r<BR>\n" );
document.write( "\n" );
document.write( "**Total:** 40\r<BR>\n" );
document.write( "\n" );
document.write( "-----\r<BR>\n" );
document.write( "\n" );
document.write( "## B) Histogram\r<BR>\n" );
document.write( "\n" );
document.write( "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. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );