document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1022940>Question 1022940</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A class has an equal number of boys and girls. The boys all got 85% on a test and the girls all got 91%. What are the mean and standard deviation of the test scores for the entire class?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #638498 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=638498\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We treat the entire class as a population.\r<BR>\n" );
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document.write( "Let n = number of boys = number of girls ==> total number of students is 2n.\r<BR>\n" );
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document.write( "==> The mean of the test scores would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+%280.85n%2B0.91n%29%2F%282n%29+=+%281.76n%29%2F%282n%29+=+0.88 ALIGN=MIDDLE  ALT=\"mu+=+%280.85n%2B0.91n%29%2F%282n%29+=+%281.76n%29%2F%282n%29+=+0.88\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2888%29 ALIGN=MIDDLE  ALT=\"highlight%2888%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >%.\r<BR>\n" );
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document.write( "To find the standard deviation, use the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma%5E2+=+%281%2F%282n%29%29sum%28x%5Bi%5D%5E2%2C+1%2C+2n+%29+-+mu%5E2 ALIGN=MIDDLE  ALT=\"sigma%5E2+=+%281%2F%282n%29%29sum%28x%5Bi%5D%5E2%2C+1%2C+2n+%29+-+mu%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the population variance.\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma%5E2+=+%281%2F%282n%29%29%28n%280.85%5E2%29%2Bn%280.91%5E2%29%29+-+0.88%5E2 ALIGN=MIDDLE  ALT=\"sigma%5E2+=+%281%2F%282n%29%29%28n%280.85%5E2%29%2Bn%280.91%5E2%29%29+-+0.88%5E2\"   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=sigma%5E2+=+%280.85%5E2%2B0.91%5E2%29%2F2+-+0.88%5E2+=+0.0009 ALIGN=MIDDLE  ALT=\"sigma%5E2+=+%280.85%5E2%2B0.91%5E2%29%2F2+-+0.88%5E2+=+0.0009\"   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=sigma+=+0.03 ALIGN=MIDDLE  ALT=\"sigma+=+0.03\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to three decimal places.\r<BR>\n" );
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document.write( "The standard deviation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.03%29 ALIGN=MIDDLE  ALT=\"highlight%280.03%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "(Note that both averages of 85% and 91% are exactly one standard deviation from the mean!) </SPAN>\n" );
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