document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175111>Question 1175111</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of patients in two hospitals A and B, the average wage of employees and the variances of wages are given below:<BR>\n" );
document.write( "           Hospital A           Hospital B<BR>\n" );
document.write( "No. of employees 50                100<BR>\n" );
document.write( "Mean wage        120               85<BR>\n" );
document.write( "Variance         9                 6<BR>\n" );
document.write( "In which hospital is the variation in the distribution of wages greater and why </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850626 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850626\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To determine which hospital has greater variation in the distribution of wages, we need to compare their **coefficients of variation (CV)**. The coefficient of variation measures the relative variability of data and is calculated as:\r<BR>\n" );
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document.write( "CV = (Standard Deviation / Mean) * 100%\r<BR>\n" );
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document.write( "**1. Calculate the Standard Deviation**\r<BR>\n" );
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document.write( "* Standard deviation is the square root of the variance.<BR>\n" );
document.write( "    * Hospital A: Standard Deviation (s_A) = √9 = 3<BR>\n" );
document.write( "    * Hospital B: Standard Deviation (s_B) = √6 ≈ 2.449\r<BR>\n" );
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document.write( "**2. Calculate the Coefficient of Variation (CV)**\r<BR>\n" );
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document.write( "* Hospital A: CV_A = (3 / 120) * 100% = 2.5%<BR>\n" );
document.write( "* Hospital B: CV_B = (2.449 / 85) * 100% ≈ 2.88%\r<BR>\n" );
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document.write( "**3. Compare the Coefficients of Variation**\r<BR>\n" );
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document.write( "* CV_B (2.88%) > CV_A (2.5%)\r<BR>\n" );
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document.write( "**Conclusion**\r<BR>\n" );
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document.write( "The variation in the distribution of wages is greater in **Hospital B**.\r<BR>\n" );
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document.write( "**Why?**\r<BR>\n" );
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document.write( "While Hospital A has a higher absolute variance (9 vs. 6), Hospital B has a higher coefficient of variation. This means that relative to the mean wage, the spread of wages is larger in Hospital B. In other words, the wages in Hospital B are more dispersed relative to their average wage compared to the wages in Hospital A.<BR>\n" );
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