document.write( "Question 320246: Use the student aga data and ,apply Chebyshev's theorem and the empirical rule - identify the intervals that will include 68 percent, 95 percent, and 99 percent of the age data. Compute and interpret the quartiles and interquartile range for the data.
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\n" ); document.write( "\n" ); document.write( "1- 42
\n" ); document.write( "2- 35
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\n" ); document.write( "6- 29
\n" ); document.write( "7- 26
\n" ); document.write( "8- 48
\n" ); document.write( "9- 37
\n" ); document.write( "10- 27
\n" ); document.write( "11- 47
\n" ); document.write( "12- 26\r
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Algebra.Com's Answer #229384 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "On your TI-83 or TI-84\r\n" );
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document.write( "Press CLEAR\r\n" );
document.write( "Press STAT\r\n" );
document.write( "Press 1\r\n" );
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document.write( "Enter the 12 numbers in L1\r\n" );
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document.write( "Press STAT\r\n" );
document.write( "Press the right arrow key to highlight CALC\r\n" );
document.write( "Press 1\r\n" );
document.write( "Press ENTER\r\n" );
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document.write( "Read the mean as x = 34.33333333\r\n" );
document.write( "Read the standard deviation as Sx=7.784989442\r\n" );
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document.write( "Chebyshev's theorem states that\r\n" );
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document.write( " of the data will lie within  standard\r\n" );
document.write( "deviations of the mean, where .\r\n" );
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document.write( "Using k=1.1, and the mean and standard deviation above, Chebyshev's \r\n" );
document.write( "theorem tells us that AT LEAST 17.3% of the data lies between 25.77 \r\n" );
document.write( "and 42.897.  In fact 83.3% of it does! \r\n" );
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document.write( "Using k=1.5, and the mean and standard deviation above, Chebyshev's \r\n" );
document.write( "theorem tells us that AT LEAST 55.5% of the data lies between 22.66 \r\n" );
document.write( "and 46.01.  In fact 83.3% of it does!\r\n" );
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document.write( "Using k=2, and the mean and standard deviation above, Chebyshev's \r\n" );
document.write( "theorem tells us that AT LEAST 75% of the data lies between 18.76 \r\n" );
document.write( "and 49.90.  In fact 100% of it does!\r\n" );
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document.write( "-----------------------------\r\n" );
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document.write( "The empirical rule says that if a histogram of the data is \r\n" );
document.write( "approximately bell-shaped, like this:\r\n" );
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document.write( "then \r\n" );
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document.write( "1. approximately 68% of the data will fall between 1 standard deviation\r\n" );
document.write( "below the mean and 1 standard deviation above the mean.\r\n" );
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document.write( "That is, if the given data is approximately bell-shaped, then 68% of\r\n" );
document.write( "the data should fall between \r\n" );
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document.write( "34.33333333 - 7.784989442 or 26.54834389\r\n" );
document.write( "and\r\n" );
document.write( "34.33333333 - 7.784989442 or 42.11832278\r\n" );
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document.write( "Actually 10 of the 12 data values fall between these, so that's %\r\n" );
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document.write( "Also\r\n" );
document.write( "2. approximately 95% of the data will fall between 2 standard deviations\r\n" );
document.write( "below the mean and 2 standard deviations above the mean.\r\n" );
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document.write( "That is, if the given data is approximately bell-shaped, then about 95% of\r\n" );
document.write( "the data should fall between \r\n" );
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document.write( "34.33333333 - 2(7.784989442) or 18.76335445\r\n" );
document.write( "and\r\n" );
document.write( "34.33333333 + 2(7.784989442) or 49.90331222\r\n" );
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document.write( "Actually all 12 of data values fall between these, so that's %.\r\n" );
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document.write( "Edwin

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