document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=449561>Question 449561</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . Find the mean, mode, median, variance and standard deviation of the following data:<BR>\n" );
document.write( "35<BR>\n" );
document.write( "45<BR>\n" );
document.write( "30<BR>\n" );
document.write( "35<BR>\n" );
document.write( "40<BR>\n" );
document.write( "25<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #309278 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=309278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "The mean is the usual <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=average ALIGN=MIDDLE  ALT=\"average\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so: add them and divide the sum by number of data\r<BR>\n" );
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document.write( "210\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210%2F6=35 ALIGN=MIDDLE  ALT=\"210%2F6=35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The mean is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35 ALIGN=MIDDLE  ALT=\"35\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The mode is the number that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=repeated ALIGN=MIDDLE  ALT=\"repeated\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+more ALIGN=MIDDLE  ALT=\"+more\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+often ALIGN=MIDDLE  ALT=\"+often\"   DISABLED_style= \"max-width:90%; height:auto;\" > than any other, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35 ALIGN=MIDDLE  ALT=\"35\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the mode.\r<BR>\n" );
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document.write( "The median is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=middle ALIGN=MIDDLE  ALT=\"middle\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+value ALIGN=MIDDLE  ALT=\"+value\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so I'll have to rewrite the list in order:\r<BR>\n" );
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document.write( "25<BR>\n" );
document.write( "30<BR>\n" );
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document.write( "40<BR>\n" );
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document.write( "There are six numbers in the list, so the middle one will be the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286+%2B+1%29+%F7+2+=+7+%F7+2+=+3.5th+ ALIGN=MIDDLE  ALT=\"%286+%2B+1%29+%F7+2+=+7+%F7+2+=+3.5th+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (3rd or 4th)number:\r<BR>\n" );
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document.write( "So, the median is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35 ALIGN=MIDDLE  ALT=\"35\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The variance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta%5E2 ALIGN=MIDDLE  ALT=\"delta%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a measure of how far each value in the data set is from the mean. Here is how it is defined:\r<BR>\n" );
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document.write( "    Subtract the mean from each value in the data. This gives you a measure of the distance of each value from the mean.\r<BR>\n" );
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document.write( "The mean is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35 ALIGN=MIDDLE  ALT=\"35\"   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=35-25=10 ALIGN=MIDDLE  ALT=\"35-25=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35-30=5 ALIGN=MIDDLE  ALT=\"35-30=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35-35=0 ALIGN=MIDDLE  ALT=\"35-35=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35-35=0 ALIGN=MIDDLE  ALT=\"35-35=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35-40=-5 ALIGN=MIDDLE  ALT=\"35-40=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35-45=-10%7D%7D%0D%0A%0D%0A%7B%7B%7B100%2B25%2B0%2B0%2B25%2B100=250%7D%7D%0D%0A%0D%0A++++Square+each+of+these+distances+%28so+that+they+are+all+positive+values%29%2C+and+add+all+of+the+squares+together.%0D%0A%7B%7B%7B100%2B25%2B0%2B0%2B25%2B100=250%7D%7D%0D%0A%0D%0A++++Divide+the+sum+of+the+squares+by+the+number+of+values+in+the+data+set.+%0D%0A%0D%0A%7B%7B%7B250%2F6=41.7%7D%7D%0D%0A%0D%0AThe+standard+deviation+%7B%7B%7Bdelta%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > is simply the (positive) square root of the variance.\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta=sqrt%2841.7%29=6.5 ALIGN=MIDDLE  ALT=\"delta=sqrt%2841.7%29=6.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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