document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199741>Question 1199741</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The highway mileage (mpg) for a sample of 9 different models of a car company can be found below.\r<BR>\n" );
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document.write( "43	31	37	44	50	40	39	25	50\r<BR>\n" );
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document.write( "Data: 43,31,37,44,50,40,39,25,50\r<BR>\n" );
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document.write( "Find the mode: \r<BR>\n" );
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document.write( "Find the midrange: \r<BR>\n" );
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document.write( "Find the range: \r<BR>\n" );
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document.write( "Estimate the standard deviation using the range rule of thumb: \r<BR>\n" );
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document.write( "Now use technology, find the standard deviation: \r<BR>\n" );
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document.write( " (Please round your answer to 2 decimal places)  </SPAN>\n" );
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document.write( "Mode = 50<BR>\n" );
document.write( "Midrange = 37.5<BR>\n" );
document.write( "Range = 25<BR>\n" );
document.write( "Standard Deviation Estimate = 6.25<BR>\n" );
document.write( "Standard Deviation More Accurate Value = 8.22\r<BR>\n" );
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document.write( "Explanation: \r<BR>\n" );
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document.write( "Let's start off by sorting the values from smallest to largest.\r<BR>\n" );
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document.write( "43,31,37,44,50,40,39,25,50<BR>\n" );
document.write( "sorts to<BR>\n" );
document.write( "25,31,37,39,40,43,44,50,50\r<BR>\n" );
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document.write( "You can sort by hand, or use technology to do so.\r<BR>\n" );
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document.write( "The most frequent value is 50 since it shows up twice, whereas everything else shows up exactly once.<BR>\n" );
document.write( "This is why the mode is 50.\r<BR>\n" );
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document.write( "Side note: multiple modes are possible. It's also possible to not have any mode at all.\r<BR>\n" );
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document.write( "Refer to the sorted set to find<BR>\n" );
document.write( "min = smallest value = 25<BR>\n" );
document.write( "max = largest value = 50\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "midrange = (min+max)/2<BR>\n" );
document.write( "midrange = (25+50)/2<BR>\n" );
document.write( "midrange = (75)/2<BR>\n" );
document.write( "midrange = 37.5\r<BR>\n" );
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document.write( "The midrange is the midpoint of the smallest and largest items. <BR>\n" );
document.write( "It's a measure of center, but it doesn't get used very much.\r<BR>\n" );
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document.write( "Despite the fact the word \"range\" is part of the word \"midrange\", the midrange is not a measure of spread. This can be slightly confusing for students.\r<BR>\n" );
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document.write( "Range = max - min<BR>\n" );
document.write( "Range = 50 - 25<BR>\n" );
document.write( "Range = 25\r<BR>\n" );
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document.write( "This is a measure of how spread out the data set is.\r<BR>\n" );
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document.write( "The range rule of thumb is where we divide the range over 4 to get an estimate of the standard deviation\r<BR>\n" );
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document.write( "range/4 = 25/4 = 6.25\r<BR>\n" );
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document.write( "Further Reading:<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.statology.org/range-rule-of-thumb/\">https://www.statology.org/range-rule-of-thumb/</a>\r<BR>\n" );
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document.write( "--------------------\r<BR>\n" );
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document.write( "When it comes to technology, it's up to you which tool you prefer. <BR>\n" );
document.write( "There are many options to pick from.\r<BR>\n" );
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document.write( "Here's one free online calculator<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.calculator.net/standard-deviation-calculator.html\">https://www.calculator.net/standard-deviation-calculator.html</a>\r<BR>\n" );
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document.write( "Be sure you go for <b><u>sample</u></b> standard deviation, and not population standard deviation. <BR>\n" );
document.write( "They're slightly different concepts.<BR>\n" );
document.write( "A sample standard deviation is used because this given data set is a sample.\r<BR>\n" );
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document.write( "Use technology to determine the sample standard deviation is roughly 8.22\r<BR>\n" );
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document.write( "This isn't really that close to 6.25 we estimated earlier, but I suppose it could be worse.\r<BR>\n" );
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document.write( "The standard deviation is also a measure of spread. This is why the range rule of thumb is somewhat loosely connected to the standard deviation.<BR>\n" );
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