document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=830238>Question 830238</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the mean of 5 observations is 20.including one new observation,the mean is 25.find the newly included observation </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #500445 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=500445\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the mean of 5 observations is 20.including one new observation,the mean is 25.find the newly included observation\r<BR>\n" );
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document.write( "Let S = sum of the first 5 observations\r<BR>\n" );
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document.write( "Since \"the mean of 5 observations is 20\", this means that S/5 = 20\r<BR>\n" );
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document.write( "S/5 = 20\r<BR>\n" );
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document.write( "S = 20*5 ... Multiply both sides by 5.\r<BR>\n" );
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document.write( "S = 100\r<BR>\n" );
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document.write( "So the sum of the first 5 observations is 100.\r<BR>\n" );
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document.write( "Now let x = measure of the newly included observation\r<BR>\n" );
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document.write( "The mean, call it m, is equal to the sum of the 6 items divided by 6. Or put another way, it's equal to the sum of the first five items (S) and that new sixth observation (x). Then you divide by 6. This gives the mean m. So,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28S%2Bx%29%2F6+=+m ALIGN=MIDDLE  ALT=\"%28S%2Bx%29%2F6+=+m\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28S%2Bx%29%2F6+=+25 ALIGN=MIDDLE  ALT=\"%28S%2Bx%29%2F6+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in that new mean m = 25\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28100%2Bx%29%2F6+=+25 ALIGN=MIDDLE  ALT=\"%28100%2Bx%29%2F6+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in S = 100\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2Bx+=+25%2A6 ALIGN=MIDDLE  ALT=\"100%2Bx+=+25%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 6.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2Bx+=+150 ALIGN=MIDDLE  ALT=\"100%2Bx+=+150\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+150-100 ALIGN=MIDDLE  ALT=\"x+=+150-100\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+50 ALIGN=MIDDLE  ALT=\"x+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Therefore, the newly included observation is <font color=\"red\">50</font>, which is the final answer. </SPAN>\n" );
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