document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190752>Question 1190752</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following data give the yearly numbers of law enforcement officers killed in the United <BR>\n" );
document.write( "States over 10 years: 164, 165, 157, 164, 152, 147, 148, 131, 147, 155, calculate sample <BR>\n" );
document.write( "variance and standard deviation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849210 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=849210\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the sample variance and standard deviation:\r<BR>\n" );
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document.write( "1. **Calculate the mean (average):**\r<BR>\n" );
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document.write( "   Mean = (164 + 165 + 157 + 164 + 152 + 147 + 148 + 131 + 147 + 155) / 10 = 1530 / 10 = 153\r<BR>\n" );
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document.write( "2. **Calculate the squared differences from the mean:**\r<BR>\n" );
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document.write( "   * (164 - 153)² = 121<BR>\n" );
document.write( "   * (165 - 153)² = 144<BR>\n" );
document.write( "   * (157 - 153)² = 16<BR>\n" );
document.write( "   * (164 - 153)² = 121<BR>\n" );
document.write( "   * (152 - 153)² = 1<BR>\n" );
document.write( "   * (147 - 153)² = 36<BR>\n" );
document.write( "   * (148 - 153)² = 25<BR>\n" );
document.write( "   * (131 - 153)² = 484<BR>\n" );
document.write( "   * (147 - 153)² = 36<BR>\n" );
document.write( "   * (155 - 153)² = 4\r<BR>\n" );
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document.write( "3. **Calculate the sum of squared differences:**\r<BR>\n" );
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document.write( "   121 + 144 + 16 + 121 + 1 + 36 + 25 + 484 + 36 + 4 = 992\r<BR>\n" );
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document.write( "4. **Calculate the sample variance:**\r<BR>\n" );
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document.write( "   Sample Variance = (Sum of Squared Differences) / (Number of Data Points - 1)\r<BR>\n" );
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document.write( "   Sample Variance = 992 / (10 - 1) = 992 / 9 ≈ 110.22\r<BR>\n" );
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document.write( "5. **Calculate the sample standard deviation:**\r<BR>\n" );
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document.write( "   Sample Standard Deviation = √(Sample Variance)\r<BR>\n" );
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document.write( "   Sample Standard Deviation = √(110.22) ≈ 10.50\r<BR>\n" );
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document.write( "Therefore, the sample variance is approximately 110.22, and the sample standard deviation is approximately 10.50. </SPAN>\n" );
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