document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011301>Question 1011301</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A civil engineer monitors water quality by measuring the<BR>\n" );
document.write( "amount of suspended solids in a sample of river water<BR>\n" );
document.write( "over 11 weeks the following observations were<BR>\n" );
document.write( "recorded 14,12,21,28, 30, 63,29, 63, 55, 19, 20<BR>\n" );
document.write( "Suspended solids (parts per million)<BR>\n" );
document.write( "(i) Find the quartiles<BR>\n" );
document.write( "(ii) Find the minimum, maximum, range and inter quartile<BR>\n" );
document.write( "range,<BR>\n" );
document.write( "(iii) Construct a box plot  </SPAN>\n" );
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document.write( "Question:<BR>\n" );
document.write( "A civil engineer monitors water quality by measuring the<BR>\n" );
document.write( "amount of suspended solids in a sample of river water<BR>\n" );
document.write( "over 11 weeks the following observations were<BR>\n" );
document.write( "recorded 14,12,21,28, 30, 63,29, 63, 55, 19, 20<BR>\n" );
document.write( "Suspended solids (parts per million)<BR>\n" );
document.write( "(i) Find the quartiles<BR>\n" );
document.write( "(ii) Find the minimum, maximum, range and inter quartile<BR>\n" );
document.write( "range,<BR>\n" );
document.write( "(iii) Construct a box plot <BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "First step is to find out <BR>\n" );
document.write( "number of observations=11<BR>\n" );
document.write( "and the sorted list in ascending order:<BR>\n" );
document.write( " 12 14 19 20 21 28 29 30 55 63 63<BR>\n" );
document.write( "(i) Quartiles are chosen such that there is an equal number of observation less than or greater than the number.  The 3 quartiles are shown below enclosed in vertical bars.<BR>\n" );
document.write( " 12 14 |19| 20 21 |28| 29 30 |55| 63 63<BR>\n" );
document.write( "Therefore the first quartile is 19, second quartile (median) is 28 and third quartile is 55.<BR>\n" );
document.write( "(ii) <BR>\n" );
document.write( "minimum is 12<BR>\n" );
document.write( "maximum is 63<BR>\n" );
document.write( "range = 63-12=51<BR>\n" );
document.write( "and the inter-quartile range (IQR) = 55-19 = 36<BR>\n" );
document.write( "(iii)<BR>\n" );
document.write( "see figure below.<BR>\n" );
document.write( "The box-plot could also be plotted horizontally.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=mathmate&illustration_name=1011301.PNG\">. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );