document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=455317>Question 455317</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the mean\r<BR>\n" );
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document.write( "Find the median\r<BR>\n" );
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document.write( "Find the mode  \r<BR>\n" );
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document.write( "Find the upper and lower quartiles\r<BR>\n" );
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document.write( "Find the range\r<BR>\n" );
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document.write( "Find the variance\r<BR>\n" );
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document.write( "Find the standard deviation\r<BR>\n" );
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document.write( "79.6,94.8,94.2,86,83.6,82,89.4,76.4,85,92.9,95.6,90.6,91.7,87.9,85.7,91.7,68,88,78.9,98.2,86.3,96\r<BR>\n" );
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document.write( "I am really having a hard time figuring this out, any help would be greatly appreciated!\r<BR>\n" );
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document.write( "THanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #312640 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=312640\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first thing to do is to get the data sorted into ascending order.  You will need them sorted to figure out the median.\r<BR>\n" );
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document.write( "68.0<BR>\n" );
document.write( "76.4<BR>\n" );
document.write( "78.9<BR>\n" );
document.write( "79.6<BR>\n" );
document.write( "82.0<BR>\n" );
document.write( "83.6<BR>\n" );
document.write( "85.0<BR>\n" );
document.write( "85.7<BR>\n" );
document.write( "86.0<BR>\n" );
document.write( "86.3<BR>\n" );
document.write( "87.9<BR>\n" );
document.write( "88.0<BR>\n" );
document.write( "89.4<BR>\n" );
document.write( "90.6<BR>\n" );
document.write( "91.7<BR>\n" );
document.write( "91.7<BR>\n" );
document.write( "92.9<BR>\n" );
document.write( "94.2<BR>\n" );
document.write( "94.8<BR>\n" );
document.write( "95.6<BR>\n" );
document.write( "96.0<BR>\n" );
document.write( "98.2\r<BR>\n" );
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document.write( "Add them up = 1922.5<BR>\n" );
document.write( "There are 22 items in the list so the mean (arithmetic mean) is the total divided by the number of items.<BR>\n" );
document.write( "1922.5/22 = 87.38636364\r<BR>\n" );
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document.write( "The median is the \"middle\" of a sorted list.  In this case the middle is between the 11th and the 12th items in the list.<BR>\n" );
document.write( "#11 = 87.9<BR>\n" );
document.write( "#12 = 88.0<BR>\n" );
document.write( "So, the median splits the difference<BR>\n" );
document.write( "(87.9+88.0)/2 = 87.95\r<BR>\n" );
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document.write( "The mode is the most frequently occurring data value.<BR>\n" );
document.write( "The only number that occurs more than once is 91.7, which occurs twice.<BR>\n" );
document.write( "So the mode = 91.7\r<BR>\n" );
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document.write( "The lower quartile is where 25% of value are less than or equal.  The upper quartile is where 75% are less than or equal.\r<BR>\n" );
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document.write( "The minimum value is 68.0<BR>\n" );
document.write( "The maximum value is 98.2<BR>\n" );
document.write( "So the range = max - min = 98.2 - 68 = 30.2\r<BR>\n" );
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document.write( "The standard deviation depends on finding the mean first.<BR>\n" );
document.write( "Then you subtract the mean from each of the values.<BR>\n" );
document.write( "Then you square each of these numbers and sum them.<BR>\n" );
document.write( "Then take the square root.<BR>\n" );
document.write( "(If you calculated the mean correctly, then the sum of each of the original values minus the mean is zero...which is not very useful.  But by squaring these differences, then you have something that you can use to describe dispersion.)<BR>\n" );
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document.write( "<tr><td>Item<td>Value<td>Value-Mean<td>Squared\r\n" );
document.write( "<tr><td>1	  <td>68.0	  <td>-19.4	      <td>375.83110\r\n" );
document.write( "<tr><td>2	  <td>76.4	  <td>-11.0	      <td>120.70019\r\n" );
document.write( "<tr><td>3	  <td>78.9	  <td> -8.5	       <td>72.01837\r\n" );
document.write( "<tr><td>4	  <td>79.6	  <td> -7.8	       <td>60.62746\r\n" );
document.write( "<tr><td>5	  <td>82.0	   <td>-5.4	       <td>29.01291\r\n" );
document.write( "<tr><td>6  	  <td>83.6	   <td>-3.8	       <td>14.33655\r\n" );
document.write( "<tr><td>7 	  <td>85.0	  <td> -2.4	        <td>5.69473\r\n" );
document.write( "<tr><td>8	  <td>85.7	   <td>-1.7	        <td>2.84382\r\n" );
document.write( "<tr><td>9	  <td>86.0	   <td>-1.4	        <td>1.92200\r\n" );
document.write( "<tr><td>10	  <td>86.3	   <td>-1.1	        <td>1.18019\r\n" );
document.write( "<tr><td>11	  <td>87.9	    <td>0.5	        <td>0.26382\r\n" );
document.write( "<tr><td>12	  <td>88.0	    <td>0.6	        <td>0.37655\r\n" );
document.write( "<tr><td>13	  <td>89.4	    <td>2.0	        <td>4.05473\r\n" );
document.write( "<tr><td>14	  <td>90.6	    <td>3.2	       <td>10.32746\r\n" );
document.write( "<tr><td>15	  <td>91.7	    <td>4.3	       <td>18.60746\r\n" );
document.write( "<tr><td>16	  <td>91.7	    <td>4.3	       <td>18.60746\r\n" );
document.write( "<tr><td>17	  <td>92.9	    <td>5.5	       <td>30.40019\r\n" );
document.write( "<tr><td>18	  <td>94.2	    <td>6.8	       <td>46.42564\r\n" );
document.write( "<tr><td>19	  <td>94.8	    <td>7.4	       <td>54.96200\r\n" );
document.write( "<tr><td>20	  <td>95.6	    <td>8.2	       <td>67.46382\r\n" );
document.write( "<tr><td>21	  <td>96.0	    <td>8.6	       <td>74.19473\r\n" );
document.write( "<tr><td>22	  <td>98.2	   <td>10.8	      <td>116.93473\r\n" );
document.write( "<tr><td>Sum	<td>1922.5	    <td>0.0	     <td>1126.8\r\n" );
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document.write( "Mean = 1922.5/22 = 87.3863<BR>\n" );
document.write( "Variance = Sum of Squared Values divided by # items minus 1<BR>\n" );
document.write( "Variance = 1126.8/21 = 53.65647186<BR>\n" );
document.write( "Std Dev = Sqrt(Variance) = Sqrt(1126.8) = 33.56763\r<BR>\n" );
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document.write( "The quartiles are 83.95 and 92.6\r<BR>\n" );
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document.write( "Done<BR>\n" );
document.write( " </SPAN>\n" );
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