document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125795>Question 1125795</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I calculate my raw score to find my z score. <BR>\n" );
document.write( "My mean is 20.87857143, median is 20, mode is 18, and my standard deviation is 4.185394023. <BR>\n" );
document.write( "What z-score would a 40 year-old have? Would it be unusual to have a 40 year-old? (yes right because nobody is 40 years old?) Determine the skew of the data\r<BR>\n" );
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document.write( "my data of ages includes: <BR>\n" );
document.write( "18,19,20,19,29,20,18<BR>\n" );
document.write( "18,18,20,19,23,18,19,18,21<BR>\n" );
document.write( "36,24,26,26,20,18,22,18,18<BR>\n" );
document.write( "18,19,20,27,21,20,18,20,18<BR>\n" );
document.write( "19,27,18,22,18,18,18,19,18<BR>\n" );
document.write( "18,19,20,19,18,19,19,31,20<BR>\n" );
document.write( "18,22,17,20,38,20,18,21<BR>\n" );
document.write( "21,31,24,23,18,19,19,21<BR>\n" );
document.write( "19,17,39,21,18,18,18,21<BR>\n" );
document.write( "32,33,17,22,19,18,20,29<BR>\n" );
document.write( "21,20,24,18,23,21,21,22<BR>\n" );
document.write( "18,20,19,18,19,18,18,18<BR>\n" );
document.write( "18,22,20,21,18,20,18,17<BR>\n" );
document.write( "21,19,25,17,20,18,25,19<BR>\n" );
document.write( "22,26,18,23,25,19,18,20<BR>\n" );
document.write( "20,19,18,22,23,21,18,18<BR>\n" );
document.write( "19,22,20,22,17,27,33,20 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #742184 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=742184\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 18,19,20,19,29,20,18,18,18,20,19,23,18,19,18,21,36,24,26,26,20,18,22,18,18,18,19,20,27,21,20,18,20,18,19,27,18,22,18,18,18,19,18,18,19,20,19,18,19,19,31,20,18,22,17,20,38,20,18,21,21,31,24,23,18,19,19,21,19,17,39,21,18,18,18,21,32,33,17,22,19,18,20,29,21,20,24,18,23,21,21,22,18,20,19,18,19,18,18,18,18,22,20,21,18,20,18,17,21,19,25,17,20,18,25,19,22,26,18,23,25,19,18,20,20,19,18,22,23,21,18,18,19,22,20,22,17,27,33,20\r<BR>\n" );
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document.write( "i looked at your data in excel.\r<BR>\n" );
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document.write( "a 40 year old would have a z-score that would be calculated as follows:\r<BR>\n" );
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document.write( "z = (x-m) / s\r<BR>\n" );
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document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard error.\r<BR>\n" );
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document.write( "the z-core for a 40 year old within this data set (the sample is assumed to be the population), would be:\r<BR>\n" );
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document.write( "z = (40 - 20.88) / 4.19 = 4.56.\r<BR>\n" );
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document.write( "the probability of getting a z-score greater than 4.56 would effectively be 0.\r<BR>\n" );
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document.write( "most z-score tables only go up to about plus or minus 3.4.\r<BR>\n" );
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document.write( "from excel, the kurtosis is about 5 and the skewness is about 2.2.\r<BR>\n" );
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document.write( "both are out of what is considered normal range, although there are differing opinions as to what is an acceptable range.\r<BR>\n" );
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document.write( "some says 2.2 for both.<BR>\n" );
document.write( "some say 1 for skewness and 3 for kurtosis.<BR>\n" );
document.write( "there are other opinions as well.\r<BR>\n" );
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document.write( "here's an example of a discussion.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.researchgate.net/post/What_is_the_acceptable_range_of_skewness_and_kurtosis_for_normal_distribution_of_data\" target = \"_blank\">https://www.researchgate.net/post/What_is_the_acceptable_range_of_skewness_and_kurtosis_for_normal_distribution_of_data</a>\r<BR>\n" );
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document.write( "fyi - i'm not a statistician so don't think what i say is from an expert.<BR>\n" );
document.write( "it's not.<BR>\n" );
document.write( "most of what was said in this discussion is way over my head.\r<BR>\n" );
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document.write( "here are the results from excel based on your data set.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/101101.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "here are the results from the z-score calculator by david m. lane.\r<BR>\n" );
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document.write( "first the raw score results.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/101102.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "then the z-score results.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/101103.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the results from the raw score test and the z-score test are consistent, as they should be.<BR>\n" );
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