document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=332224>Question 332224</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please show me how to answer this? \r<BR>\n" );
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document.write( "For a particular sample of 50 scores on a psychology exam, the following results were obtained.<BR>\n" );
document.write( "First quartile = 66  Third quartile = 92 Standard deviation = 9  Range = 49<BR>\n" );
document.write( "Mean = 74   Median = 82   Mode = 83  Midrange = 73<BR>\n" );
document.write( "Answer each of the following; show all work.<BR>\n" );
document.write( "-          What score was earned by more students than any other score? Why? <BR>\n" );
document.write( "-          What was the highest score earned on the exam? <BR>\n" );
document.write( "-          What was the lowest score earned on the exam?<BR>\n" );
document.write( "-          According to Chebyshev's Theorem, how many students scored between 56 and 92?<BR>\n" );
document.write( "-          Assume that the distribution is normal.  Based on the Empirical Rule, how many students scored between 56 and 92? <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 #238108 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=238108\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> - What score was earned by more students than any other score? Why? <BR>\n" );
document.write( "Mode= most frequently occurring score, 83<BR>\n" );
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document.write( "- What was the highest score earned on the exam? <BR>\n" );
document.write( "highest score= midrange + range/2 = 73+49/2=97.5<BR>\n" );
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document.write( "- What was the lowest score earned on the exam?<BR>\n" );
document.write( "Lowest score = midrange - range/2 = 73-49/2=48.5<BR>\n" );
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document.write( "- According to Chebyshev's Theorem, how many students scored between 56 and 92?<BR>\n" );
document.write( "largest-average=92-74=18<BR>\n" );
document.write( "this represent k=18/9=2 standard deviations from the mean<BR>\n" );
document.write( "thus CT states that \"at least\"  1-1/k^2 =1-1/4=75% of the scores will surround the average within 2 standard deviations.<BR>\n" );
document.write( "75% of 50 = 37.5 or 38 scores<BR>\n" );
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document.write( "- Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 56 and 92? <BR>\n" );
document.write( "if the data is normally distributed, approx 95% of the scores will surround the mean within 2 standard deviations<BR>\n" );
document.write( "so.. 95% of 50 =47.5 or approx 48<BR>\n" );
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