document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1152373>Question 1152373</A>: <I><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "Which of the following numbers would be an outlier if added to the data set below?<BR>\n" );
document.write( "507, 586, 499, 542, 615, 600, 561, 519<BR>\n" );
document.write( "487<BR>\n" );
document.write( "380<BR>\n" );
document.write( "610<BR>\n" );
document.write( "535 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #774378 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=774378\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=507 ALIGN=MIDDLE  ALT=\"507\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=586 ALIGN=MIDDLE  ALT=\"586\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=499 ALIGN=MIDDLE  ALT=\"499\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=542 ALIGN=MIDDLE  ALT=\"542\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=615 ALIGN=MIDDLE  ALT=\"615\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600 ALIGN=MIDDLE  ALT=\"600\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=561 ALIGN=MIDDLE  ALT=\"561\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=519 ALIGN=MIDDLE  ALT=\"519\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the sample size <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+8 ALIGN=MIDDLE  ALT=\"n+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > is even, we have that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B1%29%2F2+=+%288%2B1%29%2F2+=+4.5%28n%2B1%29%2F2=%288%2B1%29%2F2=4.5 ALIGN=MIDDLE  ALT=\"%28n%2B1%29%2F2+=+%288%2B1%29%2F2+=+4.5%28n%2B1%29%2F2=%288%2B1%29%2F2=4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which is not an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=integer ALIGN=MIDDLE  ALT=\"integer\"   DISABLED_style= \"max-width:90%; height:auto;\" > value, the median is computing by taking the average of the values at the positions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >th and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=median+=+%28+542+%2B+561%29%2F2+=+551.5 ALIGN=MIDDLE  ALT=\"median+=+%28+542+%2B+561%29%2F2+=+551.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q%5B1%5D ALIGN=MIDDLE  ALT=\"Q%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have to compute the following position:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q%5B1%5D+=+%28n%2B1%29%2825%2F00%29+=+%288%2B1%29+%281%2F4%29+=+9%2A0.25=2.25 ALIGN=MIDDLE  ALT=\"Q%5B1%5D+=+%28n%2B1%29%2825%2F00%29+=+%288%2B1%29+%281%2F4%29+=+9%2A0.25=2.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.25 ALIGN=MIDDLE  ALT=\"2.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=integer ALIGN=MIDDLE  ALT=\"integer\"   DISABLED_style= \"max-width:90%; height:auto;\" > number, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q%5B1%5D ALIGN=MIDDLE  ALT=\"Q%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is computed by interpolating between the values located in the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >nd and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >rd positions :\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q%5B1%5D=507%2B%282.25-2%29%2A%28519-507%29=510 ALIGN=MIDDLE  ALT=\"Q%5B1%5D=507%2B%282.25-2%29%2A%28519-507%29=510\"   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=Q%5B3%5D=%28n%2B1%29+%28100%2F75%29=%288%2B1%29+0.75=6.75 ALIGN=MIDDLE  ALT=\"Q%5B3%5D=%28n%2B1%29+%28100%2F75%29=%288%2B1%29+0.75=6.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.75 ALIGN=MIDDLE  ALT=\"6.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not an integer number, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q%5B3%5D ALIGN=MIDDLE  ALT=\"Q%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is computed by interpolating between the values located in the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >th and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >th positions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q%5B3%5D=586%2B%286.75-6%29%2A%28600-586%29=596.5 ALIGN=MIDDLE  ALT=\"Q%5B3%5D=586%2B%286.75-6%29%2A%28600-586%29=596.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The interquartile range is: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=IQR=Q3-Q1=596.5-510=86.5 ALIGN=MIDDLE  ALT=\"IQR=Q3-Q1=596.5-510=86.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, we can compute the lower and upper limits for outliers:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Lower=Q%5B1%5D-1.5%2AIQR=510-1.5%2A86.5=380.25 ALIGN=MIDDLE  ALT=\"Lower=Q%5B1%5D-1.5%2AIQR=510-1.5%2A86.5=380.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Upper=Q%5B3%5D%2B1.5%2AIQR=596.5%2B1.5%2A86.5=726.25 ALIGN=MIDDLE  ALT=\"Upper=Q%5B3%5D%2B1.5%2AIQR=596.5%2B1.5%2A86.5=726.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In this case since all the outcomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+ ALIGN=MIDDLE  ALT=\"X+\"   DISABLED_style= \"max-width:90%; height:auto;\" >are within the values of <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Lower+=+380.25 ALIGN=MIDDLE  ALT=\"Lower+=+380.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Upper+=+726.25 ALIGN=MIDDLE  ALT=\"Upper+=+726.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NO ALIGN=MIDDLE  ALT=\"NO\"   DISABLED_style= \"max-width:90%; height:auto;\" > outliers.\r<BR>\n" );
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document.write( "answer: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NO ALIGN=MIDDLE  ALT=\"NO\"   DISABLED_style= \"max-width:90%; height:auto;\" > outliers<BR>\n" );
document.write( "Set of outliers: {} - empty set  \r<BR>\n" );
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document.write( " </SPAN>\n" );
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