document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179844>Question 1179844</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For this freqeuncy distribution find the: \r<BR>\n" );
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document.write( "A. Sample mean: (round to two decimal places)\r<BR>\n" );
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document.write( "B. Sample Standard Deviation (round to two decimal places)\r<BR>\n" );
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document.write( "X      Frequency\r<BR>\n" );
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document.write( "1        3<BR>\n" );
document.write( "2        7<BR>\n" );
document.write( "4        10<BR>\n" );
document.write( "6        8<BR>\n" );
document.write( "7        4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850165 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=850165\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the sample mean and sample standard deviation for the given frequency distribution:\r<BR>\n" );
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document.write( "**A. Sample Mean (x̄):**\r<BR>\n" );
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document.write( "1.  **Calculate the sum of (x * frequency):**<BR>\n" );
document.write( "    * (1 * 3) + (2 * 7) + (4 * 10) + (6 * 8) + (7 * 4) = 3 + 14 + 40 + 48 + 28 = 133\r<BR>\n" );
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document.write( "2.  **Calculate the total frequency (n):**<BR>\n" );
document.write( "    * 3 + 7 + 10 + 8 + 4 = 32\r<BR>\n" );
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document.write( "3.  **Calculate the sample mean:**<BR>\n" );
document.write( "    * x̄ = (sum of (x * frequency)) / n<BR>\n" );
document.write( "    * x̄ = 133 / 32 ≈ 4.16\r<BR>\n" );
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document.write( "**B. Sample Standard Deviation (s):**\r<BR>\n" );
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document.write( "1.  **Calculate (x - x̄)² for each x:**<BR>\n" );
document.write( "    * (1 - 4.16)² ≈ 9.99<BR>\n" );
document.write( "    * (2 - 4.16)² ≈ 4.67<BR>\n" );
document.write( "    * (4 - 4.16)² ≈ 0.03<BR>\n" );
document.write( "    * (6 - 4.16)² ≈ 3.39<BR>\n" );
document.write( "    * (7 - 4.16)² ≈ 8.07\r<BR>\n" );
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document.write( "2.  **Multiply each (x - x̄)² by its frequency:**<BR>\n" );
document.write( "    * 9.99 * 3 ≈ 29.97<BR>\n" );
document.write( "    * 4.67 * 7 ≈ 32.69<BR>\n" );
document.write( "    * 0.03 * 10 ≈ 0.3<BR>\n" );
document.write( "    * 3.39 * 8 ≈ 27.12<BR>\n" );
document.write( "    * 8.07 * 4 ≈ 32.28\r<BR>\n" );
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document.write( "3.  **Calculate the sum of the results from step 2:**<BR>\n" );
document.write( "    * 29.97 + 32.69 + 0.3 + 27.12 + 32.28 = 122.36\r<BR>\n" );
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document.write( "4.  **Divide by (n - 1):**<BR>\n" );
document.write( "    * 122.36 / (32 - 1) = 122.36 / 31 ≈ 3.947\r<BR>\n" );
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document.write( "5.  **Take the square root:**<BR>\n" );
document.write( "    * s = √3.947 ≈ 1.99\r<BR>\n" );
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document.write( "**Answers:**\r<BR>\n" );
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document.write( "A. Sample mean: 4.16<BR>\n" );
document.write( "B. Sample standard deviation: 1.99<BR>\n" );
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