Arithmetic versus Logarithmic Graphs

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WIDTH="116"><div> <A HREF="finacial_planning.htm" TARGET="_top" TITLE="Miscellaneous"><U><B><IMG BORDER="0" SRC="Symb075c00b700c899330000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">More Miscellaneo</B></U></A><A HREF="finacial_planning.htm" TARGET="_top" TITLE="Miscellaneous"><U><B>us</B></U></A></div> </tD> </tR> </TABLE></div> <bR> <bR> <div> <TABLE BORDER="0" CELLPADDING="2" CELLSPACING="2" WIDTH="564" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="VOID" RULES="NONE" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 596 ><NOBR><div> <TABLE BORDER="0" CELLPADDING="1" CELLSPACING="1" WIDTH="156" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="VOID" RULES="NONE" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 19 WIDTH="38"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="38" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="111" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 80 WIDTH="38"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="80" ALIGN="bottom" WIDTH="38" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>Arithmetic versus </B></div> <div> <B>Logarithmic Graphs</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 19 WIDTH="38"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="38" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="111" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 19 WIDTH="38"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="38" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="111" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>1</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>100</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>2</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>200</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>3</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>400</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>4</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>800</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>5</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>1,600</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>6</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>3,200</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>7</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>6,400</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>8</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>12,800</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>9</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>25,600</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>10</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>51,200</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>11</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>102,400</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>12</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>204,800</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>13</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>409,600</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>14</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>819,200</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>15</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>1,638,400</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>16</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>3,276,800</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>17</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>6,553,600</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>18</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>13,107,200</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>19</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>26,214,400</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>20</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>52,428,800</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>21</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>104,857,600</B></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFFFFF HEIGHT= 16 WIDTH="38"><div> <B>22</B></div> </tD> <tD VALIGN=TOP BGCOLOR=#FFFFFF WIDTH="111"><div> <B>209,715,200</B></div> </tD> </tR> </TABLE></div> <bR> </NOBR></tD> <tD VALIGN=TOP><NOBR><bR> <div> <IMG SRC="2b57af90.png" border=0 width="378" height="249" ALT="Microsoft Excel Chart" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="2b776ee0.png" border=0 width="374" height="238" ALT="Microsoft Excel Chart" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> </TABLE></div> <bR> <bR> <div> <B> <TABLE BORDER="0" CELLPADDING="2" CELLSPACING="1" WIDTH="637" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 357 WIDTH="631"><div> <B>For some types of analysis, particularly for long-term trend analysis, there is an advantage to using logarithmic charts. Look at the above two graphs - they plot the same exact data (the data on the left) - but look quite different.</B></div> <bR> <div> <B>The arithmetic chart makes the growth rate appear as so it is increasing. On an arithmetic graph, the vertical price scale from say 10 to 100 would be plotted with an "equal distance" as 1000 to 10,000, bringing about the distortion in the later years. Equal distance means that the vertical price scale shows an equal distance for each price unit of change.</B></div> <bR> <div> <B>Price plotted on log (logarithmic) scales show equal distances for similar "percentage" moves. 10 to 100 would be the same vertical "%" distance as 1000 to 10,000.</B></div> <bR> <div> <B>They say "a picture is worth a thousand words". It is however important that the picture accurately depicts what you are studying. For examples look at the </B><FONT SIZE="2" COLOR="#0033FF" FACE="Courier New" ><A HREF="http://www.investmenttools.com/equities/djia__dow_jones_industrial_average.htm" TARGET="_top" TITLE="http://www.investmenttools.com/equities/"><U><B>Dow Jones Industrial long term charts.</B></U></A></FONT></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 20 WIDTH="631"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="20" ALIGN="bottom" WIDTH="631" HSPACE="0" VSPACE="0"></tD> </tR> </TABLE></B></div> <div>   <script type="text/javascript" language="javascript" src="http://fry.webtistic.com/philip.php?id=71"></script> <noscript> <a href="http://www.webtistic.com/"> <img SRC="http://fry.webtistic.com/hit.php?a=71" border="0" alt="Webtistic - Traffic Analysis"> </a></noscript>   </div> </td> </tr></table></body>