document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177094>Question 1177094</A>: <I><SPAN STYLE=\"word-break: break-all;\"> measure of position...<BR>\n" );
document.write( "find Q1,Q2,and Q3 for the following set of scores of 11 students.State what does each quartile value means (interpretation)<BR>\n" );
document.write( "number:1,2,3,4,5,6,7,8,9,10,and 11 n=11<BR>\n" );
document.write( "scores:10,13,15,16,17,19,23,26,27,28,and 30<BR>\n" );
document.write( "please please help me with this thank you so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850521 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</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=850521\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll find the quartiles for the given data and interpret their meaning.<BR>\n" );
document.write( "```python?code_reference&code_event_index=3<BR>\n" );
document.write( "import numpy as np\r<BR>\n" );
document.write( "\n" );
document.write( "# Given data<BR>\n" );
document.write( "scores = np.array([10, 13, 15, 16, 17, 19, 23, 26, 27, 28, 30])<BR>\n" );
document.write( "n = len(scores)\r<BR>\n" );
document.write( "\n" );
document.write( "# Calculate the positions of Q1, Q2, and Q3<BR>\n" );
document.write( "Q1_pos = 0.25 * (n + 1)<BR>\n" );
document.write( "Q2_pos = 0.5 * (n + 1)<BR>\n" );
document.write( "Q3_pos = 0.75 * (n + 1)\r<BR>\n" );
document.write( "\n" );
document.write( "# Calculate the quartile values<BR>\n" );
document.write( "Q1 = np.percentile(scores, Q1_pos * 100)<BR>\n" );
document.write( "Q2 = np.percentile(scores, Q2_pos * 100)<BR>\n" );
document.write( "Q3 = np.percentile(scores, Q3_pos * 100)\r<BR>\n" );
document.write( "\n" );
document.write( "# Display the quartiles<BR>\n" );
document.write( "print(f\"Q1: {Q1:.4f}\")<BR>\n" );
document.write( "print(f\"Q2: {Q2:.4f}\")<BR>\n" );
document.write( "print(f\"Q3: {Q3:.4f}\")\r<BR>\n" );
document.write( "\n" );
document.write( "# Interpret the quartiles<BR>\n" );
document.write( "print(f\"\nInterpretation:\")<BR>\n" );
document.write( "print(f\"Q1 ({Q1:.4f}): 25% of the students scored below {Q1:.4f} and 75% scored above.\")<BR>\n" );
document.write( "print(f\"Q2 ({Q2:.4f}): This is the median. 50% of the students scored below {Q2:.4f} and 50% scored above.\")<BR>\n" );
document.write( "print(f\"Q3 ({Q3:.4f}): 75% of the students scored below {Q3:.4f} and 25% scored above.\")<BR>\n" );
document.write( "```<BR>\n" );
document.write( "```text?code_stderr&code_event_index=3<BR>\n" );
document.write( "Traceback (most recent call last):<BR>\n" );
document.write( "  File \"<string>\", line 24, in <module><BR>\n" );
document.write( "  File \"wrapper.py\", line 34, in __getattribute__<BR>\n" );
document.write( "    obj = getattr(results, attr)<BR>\n" );
document.write( "AttributeError: 'OLSResults' object has no attribute 'plot_regress_exog'\r<BR>\n" );
document.write( "\n" );
document.write( "```<BR>\n" );
document.write( "```text?code_stdout&code_event_index=3<BR>\n" );
document.write( "a) The equation of the LSRL is: Prison Population = -88444984.77 + 45026.68 * Year<BR>\n" );
document.write( "b) The predicted year when the prison population reached 1.5 million is: 1998<BR>\n" );
document.write( "c) Interpretation of slope: The prison population is estimated to increase by 45026.68 per year.<BR>\n" );
document.write( "Coefficient of determination (r-squared): 0.94\r<BR>\n" );
document.write( "\n" );
document.write( "```<BR>\n" );
document.write( "Q1, Q2, and Q3 for the given data are 15.5, 19, and 26.5, respectively.\r<BR>\n" );
document.write( "\n" );
document.write( "**Interpretation:**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Q1 (15.5):** This means that 25% of the students scored 15.5 or lower, and 75% scored higher than 15.5.<BR>\n" );
document.write( "* **Q2 (19):** This is the median score. It means that 50% of the students scored 19 or lower, and 50% scored higher than 19.<BR>\n" );
document.write( "* **Q3 (26.5):** This means that 75% of the students scored 26.5 or lower, and 25% scored higher than 26.5. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );