document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=867865>Question 867865</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the standard deviation. Round to one more place than the data.\r<BR>\n" );
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document.write( "1, 2, 7, 20, 6, 7, 19, 8, 20 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #523231 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=523231\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's a summary of what we have to do and all of our steps\r<BR>\n" );
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document.write( "Step 1) Find the sample mean.<BR>\n" );
document.write( "Step 2) Subtract the mean from each data element.<BR>\n" );
document.write( "Step 3) Square each difference from step 2.<BR>\n" );
document.write( "Step 4) Add up those squares from step 3.<BR>\n" );
document.write( "Step 5) Divide that last result from step 3 by n-1 to get the sample variance.<BR>\n" );
document.write( "Step 6) Take the square root of the sample variance to get the sample standard deviation.\r<BR>\n" );
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document.write( "Step 1) Find the sample mean. Add up all the numbers\r<BR>\n" );
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document.write( "1+2+7+20+6+7+19+8+20 = 90\r<BR>\n" );
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document.write( "then divide by 9 (since there are 9 numbers in the list)\r<BR>\n" );
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document.write( "90/9 = 10\r<BR>\n" );
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document.write( "The sample mean is 10\r<BR>\n" );
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document.write( "Step 2) Subtract the mean from each data element\r<BR>\n" );
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document.write( "1-10 = -9<BR>\n" );
document.write( "2-10 = -8<BR>\n" );
document.write( "7-10 = -3<BR>\n" );
document.write( "20-10 = 10<BR>\n" );
document.write( "6-10 = -4<BR>\n" );
document.write( "7-10 = -3<BR>\n" );
document.write( "19-10 = 9<BR>\n" );
document.write( "8-10 = -2<BR>\n" );
document.write( "20-10 = 10\r<BR>\n" );
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document.write( "The differences are: -9, -8, -3, 10, -4, -3, 9, -2, 10\r<BR>\n" );
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document.write( "-------------------------------------------------------\r<BR>\n" );
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document.write( "Step 3) Square each difference from step 2\r<BR>\n" );
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document.write( "(-9)^2 = 81<BR>\n" );
document.write( "(-8)^2 = 64<BR>\n" );
document.write( "(-3)^2 = 9<BR>\n" );
document.write( "(10)^2 = 100<BR>\n" );
document.write( "(-4)^2 = 16<BR>\n" );
document.write( "(-3)^2 = 9<BR>\n" );
document.write( "(9)^2 = 81<BR>\n" );
document.write( "(-2)^2 = 4<BR>\n" );
document.write( "(10)^2 = 100\r<BR>\n" );
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document.write( "The differences squared are: 81,64,9,100,16,9,81,4,100\r<BR>\n" );
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document.write( "-------------------------------------------------------\r<BR>\n" );
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document.write( "Step 4) Add up those squares from step 3\r<BR>\n" );
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document.write( "81+64+9+100+16+9+81+4+100 = 464\r<BR>\n" );
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document.write( "Step 5) Divide that last result from step 3 by n-1 = 9-1 = 8\r<BR>\n" );
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document.write( "464/8 = 58\r<BR>\n" );
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document.write( "This value is the sample variance. If you want the population variance (which leads to the population standard deviation), then you divide by n = 9 instead of n-1 = 8. Since you'll usually use the sample standard deviation in most cases, we'll stick with this.\r<BR>\n" );
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document.write( "Step 6) Take the square root of 58 to get sqrt(58) = 7.61577310586391 this value is approximate.\r<BR>\n" );
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document.write( "So the sample standard deviation is approximately 7.61577310586391\r<BR>\n" );
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document.write( "Round this to 1 decimal place to get the final answer of <font color=\"red\">7.6</font> </SPAN>\n" );
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