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 ‫ﻣﻌﺮﻓﯽ و آﻣﻮزش اﻧﻮاع ﻧﻤﻮدار‬
‫‪Chart & Diagram Training‬‬


                 ‫اراﺋﻪ دﻫﻨﺪه: ﮐﯿﻮان ﺟﻌﻔﺮي ﻓﺸﺎرﮐﯽ‬
                                ‫اﻧﺪﯾﺸﮑﺪه ﮐﯿﻮان‬


                  ‫‪www.k1j.ir‬‬                ‫وﺑﮕﺎه:‬
                  ‫‪k1j@k1j.ir‬‬     ‫ﭘﺴﺖ اﻟﮑﺘﺮوﻧﯿﮏ:‬




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‫ﺑﻪ ﻧﺎم ﯾﮕﺎﻧﻪ ي داﻧﺎ و ﺗﻮاﻧﺎ‬




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                                          ‫ﻣﻘﺪﻣﻪ‬
                                     ‫ﻣﻔﺎﻫﯿﻢ ﭘﺎﯾﻪ‬
                            ‫اﻫﺪاف ﺗﺮﺳﯿﻢ ﻧﻤﻮدار‬
                 ‫اﺳﺘﺎﻧﺪاردﻫﺎ و ﻗﻮاﻧﯿﻦ رﺳﻢ ﻧﻤﻮدار‬


                                 ‫1- اﻧﻮاع ﻧﻤﻮدار‬
                                        ‫ﺳﺘﻮﻧﯽ‬
                                          ‫ﺧﻄﯽ‬
                                      ‫داﯾﺮه اي‬

    ‫2- ﺗﺮﺳﯿﻢ ﻧﻤﻮدارﻫﺎي ﻣﺨﺘﻠﻒ در ﻧﺮم اﻓﺰار اﮐﺴﻞ‬

           ‫3- ﺗﺮﺳﯿﻢ ﻧﻤﻮدار در ﻧﺮم اﻓﺰارﻫﺎي دﯾﮕﺮ‬




‫3‬




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      ‫اﻧﺘﻘﺎل ﭘﯿﺎم ﺑﺎ ﯾﮏ ﻧﻤﻮدار‬

                        ‫ﻣﻘﺎﯾﺴﻪ آﯾﺘﻤﯽ ﺑﺎ آﯾﺘﻤﯽ دﯾﮕﺮ‬    ‫•‬
                       ‫ﻣﻘﺎﯾﺴﻪ داده ﻫﺎ ﺑﺮ اﺳﺎس زﻣﺎن‬    ‫•‬
          ‫ﻣﻘﺎﯾﺴﺎت ﻧﺴﺒﯽ )ﻣﺎﻧﻨﺪ ﻧﻤﻮدار ﻫﺎي داﯾﺮه اي(‬    ‫•‬
             ‫ﻣﻘﺎﯾﺴﻪ رواﺑﻂ داده اي )ﻣﺎﻧﻨﺪ ﻧﻤﻮدار ‪(XY‬‬   ‫•‬
                                     ‫ﻣﻘﺎﯾﺴﻪ ﺑﺴﺎﻣﺪي‬    ‫•‬
‫ﻣﺸﺨﺺ ﮐﺮدن “داده ﭘﺮاﮐﻨﺪه” ﯾﺎ ﻣﻮﻗﻌﯿﺖ ﻫﺎ ﻏﯿﺮ ﻣﻌﻤﻮل‬       ‫•‬




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               ‫اﻧﺘﺨﺎب ﻧﻮع ﻧﻤﻮدار‬

‫• از ﻧﻤﻮداري اﺳﺘﻔﺎده ﮐﻨﯿﺪ ﮐﻪ ﭘﯿﺎم ﺷﻤﺎ را ﺑﻪ ﺳﺎده ﺗﺮﯾﻦ و دﻗﯿﻖ‬
                                ‫ﺗﺮﯾﻦ ﺷﮑﻞ ﻣﻤﮑﻦ ﺑﯿﺎن ﮐﻨﺪ.‬




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           ‫ﺗﻌﺮﯾﻒ ﻧﻤﻮدار-اﻧﻮاع ﻧﻤﻮدار‬
  ‫ﺑﻪ ﻧﻤﺎﯾﺶ ﺑﺼﺮي ﻣﻔﺎﻫﯿﻢ، اﯾﺪه ﻫﺎ، ﺳﺎﺧﺘﺎرﻫﺎ، رواﺑﻂ، دادهﻫﺎي آﻣﺎري و ﻏﯿﺮه ﺑﻪ‬
‫ﮔﻮﻧﻪاي ﺳﺎده و ﺷﮑﻞ ﯾﺎﻓﺘﻪ ﻧﻤﻮدار ﻣﯽﮔﻮﯾﻨﺪ. از ﻧﻤﻮدارﻫﺎ ﺑﺮاي ﺳﺎده ﮐﺮدن و‬
                      ‫ﻣﻠﻤﻮس ﮐﺮدن ﻣﻮﺿﻮﻋﺎت ﮔﻮﻧﺎﮔﻮن اﺳﺘﻔﺎده ﻣﯽﺷﻮد.‬

                      ‫ﺳﻄﺤﯽ‬               ‫ﺳﺘﻮﻧﯽ: ﺳﺘﻮﻧﯽ 2 ﺑﻌﺪي، ﺳﺘﻮﻧﯽ 3‬
                      ‫داﮔﻨﺎت‬              ‫ﺑﻌﺪي، ﻣﯿﻠﻪ اي، ﻣﺨﺮوﻃﯽ، ﻫﺮﻣﯽ‬
                 ‫ﺣﺒﺎﺑﯽ، ﺗﻮﭘﯽ‬             ‫ﺧﻄﯽ)روﻧﺪ(: ﺧﻄﯽ 2 ﺑﻌﺪي، ﺧﻄﯽ‬
                        ‫رادار‬                                   ‫3 ﺑﻌﺪي‬
                       ‫ﻓﺼﻠﯽ‬                ‫ﭘﺎي: ﭘﺎي 2 ﺑﻌﺪي، ﭘﺎي 3 ﺑﻌﺪي‬
                       ‫ﻧﺮﻣﺎل‬            ‫ﻧﻮاري)ﺑﺎر(: ﻧﻮاري 2 ﺑﻌﺪي، ﻧﻮاري‬
                    ‫ﺧﻂ زﻣﺎن‬             ‫3 ﺑﻌﺪي، ﻣﯿﻠﻪ اي، ﻣﺨﺮوﻃﯽ، ﻫﺮﻣﯽ‬
                ‫اﺳﺘﺨﻮان ﻣﺎﻫﯽ‬                    ‫ﻣﺤﯿﻄﯽ: 2 ﺑﻌﺪي، 3 ﺑﻌﺪي‬
                        ‫ﮔﺎﻧﺖ‬                   ‫ﭘﺮاﮐﻨﺪﮔﯽ )‪ :(X-Y‬ﻧﻘﻄﻪ اي،‬
                 ‫ﺟﺮﯾﺎن ﻧﻘﺪي‬                                      ‫ﺳﻬﺎﻣﯽ‬




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‫ﻧﻤﻮدارﻫﺎي اﮐﺴﻞ‬

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‫ﻧﻤﻮدارﻫﺎي اﮐﺴﻞ‬




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‫اﻧﻮاع ﻧﻤﻮدارﻫﺎ‬




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‫اﻧﻮاع ﻧﻤﻮدارﻫﺎ‬




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‫ﻧﻤﻮدارﻫﺎي ﺳﺘﻮﻧﯽ )‪(Column‬‬




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         ‫ﻧﻤﻮدارﻫﺎي ﺳﺘﻮﻧﯽ )‪(Column‬‬

 ‫• ﻫﺮ ﯾﮏ از ﻧﻘﺎط داده اي را ﺑﻪ ﺻﻮرت ﯾﮏ ﺳﺘﻮن ﻋﻤﻮدي ﻧﺸﺎن‬
                      ‫ﻣﯽ دﻫﺪ. ارﺗﻔﺎع ﻧﻤﺎﯾﺎﻧﮕﺮ ﻣﻘﺪار ﻣﯽ ﺑﺎﺷﺪ.‬
     ‫• ﻧﻘﺎط داده اي ﻣﺮﺑﻮط ﺑﻪ ﻫﺮ ﺳﺮي از داده ﻣﯽ ﺗﻮاﻧﻨﺪ ﺑﺮ روي‬
                                        ‫ﻫﻤﺪﯾﮕﺮ ﭘﺸﺘﻪ ﺷﻮﻧﺪ.‬
‫• اﻏﻠﺐ ﺟﻬﺖ ﻣﻘﺎﯾﺴﻪ آﯾﺘﻢ ﻫﺎي ﻣﺠﺰا ﺑﻪ ﮐﺎر ﻣﯽ روﻧﺪ و ﻣﯽ ﺗﻮاﻧﻨﺪ‬
       ‫ﺗﻔﺎوت ﻫﺎي ﻣﻮﺟﻮد ﺑﯿﻦ آﯾﺘﻢ ﻫﺎي ﯾﮑﺴﺮي و ﯾﺎ ﺳﺮي ﻫﺎي‬
                                     ‫ﭼﻨﺪﮔﺎﻧﻪ را ﻧﺸﺎن دﻫﻨﺪ.‬




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‫ﻧﻤﻮدارﻫﺎي ﻣﯿﻠﻪ اي )‪(Bar‬‬




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            ‫ﻧﻤﻮدارﻫﺎي ﻣﯿﻠﻪ اي )‪(Bar‬‬

   ‫• ﺷﺒﯿﻪ ﻧﻤﻮدار ﺳﺘﻮﻧﯽ اﺳﺖ ﮐﻪ 09 درﺟﻪ در ﺟﻬﺖ ﻋﻘﺮﺑﻪ ﻫﺎي‬
                                      ‫ﺳﺎﻋﺖ ﭼﺮﺧﯿﺪه اﺳﺖ.‬
 ‫• ﻣﺰﯾﺖ آن ﺧﻮاﻧﺪن آﺳﺎن ﺗﺮ ﻋﻨﺎوﯾﻦ و ﺑﺮﭼﺴﺐ ﻫﺎي ﻫﺮ ﮔﺮوه ﻣﯽ‬
                                                    ‫ﺑﺎﺷﺪ.‬
‫• ﺑﺮﺧﻼف ﻧﻤﻮدار ﺳﺘﻮﻧﯽ، در ﻧﻤﻮدار ﻣﯿﻠﻪ اي ﻫﯿﭻ ﻧﻤﻮدار ﻓﺮﻋﯽ ﮐﻪ‬
  ‫ﻫﻤﺮاه ﺑﺎ ﻣﺤﻮر ﺳﻮم ﭼﻨﺪﯾﻦ ﺳﺮي را ﻧﻤﺎﯾﺶ دﻫﺪ، ﻣﻮﺟﻮد ﻧﻤﯽ‬
   ‫ﺑﺎﺷﺪ. )ﻫﯿﭻ ﻧﻮع ﻧﻤﻮدار ﻓﺮﻋﯽ ‪ 3D-Bar Chart‬وﺟﻮد ﻧﺪارد.‬




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‫ﻧﻤﻮدارﻫﺎي ﺧﻄﯽ‬




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    ‫ﻧﻤﻮدارﻫﺎي ﺧﻄﯽ‬

‫• اﻏﻠﺐ ﺑﺮاي رﺳﻢ داده ﻫﺎي ﭘﯿﻮﺳﺘﻪ ﺑﻪ ﮐﺎر ﻣﯽ رود‬
         ‫• ﺑﺮاي ﺗﻌﯿﯿﻦ ﺟﻬﺖ و ﮔﺮاﯾﺶ ﻣﻔﯿﺪ اﺳﺖ‬
                        ‫• ﺗﺮﺳﯿﻢ ﻓﺮوش ﻣﺎﻫﯿﺎﻧﻪ‬




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‫ﻧﻤﻮدار ﻣﻘﺎﯾﺴﻪ اي ﺳﺎل ﻫﺎ-ﻓﺼﻞ ﻫﺎ و ﻣﺎه ﻫﺎ‬




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‫ﻣﻘﺎﯾﺴﻪ روﻧﺪﻫﺎي ﭼﻨﺪ ﺳﺎل ﻗﯿﻤﺖ ﻃﻼ‬




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‫ﻧﻤﻮدار ﮐﻨﺘﺮﻟﯽ‬




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‫ﻧﻤﻮدارﻫﺎي داﯾﺮه اي‬




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     ‫ﻧﻤﻮدارﻫﺎي داﯾﺮه اي )‪(Pie‬‬

‫ﺑﺮاي ﻧﻤﺎﯾﺶ ﺳﻬﻢ ﯾﺎ اﺑﻌﺎد ﻧﺴﺒﯽ از ﮐﻞ اﺳﺘﻔﺎده ﻣﯽ ﺷﻮد.‬      ‫•‬
          ‫ﻓﻘﻂ ﻣﯽ ﺗﻮان از ﯾﮏ ﺳﺮي داده اﺳﺘﻔﺎده ﮐﺮد.‬       ‫•‬
             ‫ﺑﺮاي ﻧﻘﺎط داده اي ﮐﻮﭼﮏ ﻣﻮﺛﺮﺗﺮ ﻫﺴﺘﻨﺪ.‬       ‫•‬
     ‫ﻧﺒﺎﯾﺪ ﺑﯿﺶ از 5 ﯾﺎ 6 ﻧﻘﻄﻪ ي داده اي اﺳﺘﻔﺎده ﮐﺮد.‬    ‫•‬
                   ‫ﺑﺎﯾﺪ ﺗﻤﺎم ﻣﻘﺎدﯾﺮ اﻋﺪاد ﻣﺜﺒﺖ ﺑﺎﺷﻨﺪ.‬   ‫•‬




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‫ﻧﻤﻮدارﻫﺎي ﭘﺮاﮐﻨﺪﮔﯽ ﯾﺎ ﻣﺨﺘﺼﺎﺗﯽ )‪(XY‬‬




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  ‫ﻧﻤﻮدارﻫﺎي ﻣﺨﺘﺼﺎﺗﯽ ﯾﺎ ﭘﺮاﮐﻨﺪﮔﯽ )‪(XY‬‬

                    ‫ﻫﺮ دو ﻣﺤﻮر ﻧﺸﺎن دﻫﻨﺪه ﻣﻘﺪار ﻫﺴﺘﻨﺪ‬        ‫•‬
        ‫ﺑﺮاي ﻧﺸﺎن دادن رواﺑﻂ ﺑﯿﻦ دو ﻣﺘﻐﯿﯿﺮ ﺑﻪ ﮐﺎر ﻣﯽ رود‬     ‫•‬
  ‫ﻣﺜﺎل: رواﺑﻂ ﺑﯿﻦ ﻓﺮوش )ﻣﺤﻮر اﻓﻘﯽ( . ﻓﺮوش واﻗﻌﯽ )ﻣﺤﻮر‬        ‫•‬
                                                 ‫ﻋﻤﻮدي(‬
‫ﺗﻮﺟﻪ: ﺑﺎ اﯾﻨﮑﻪ ﻧﻘﺎط داده ﻫﺎ ﻣﻄﺎﺑﻖ ﺑﺎ زﻣﺎن اﺳﺖ، اﻣﺎ درك اﯾﻦ‬   ‫•‬
‫ﻣﻄﻠﺐ ﮐﻪ اﻃﻼﻋﺎت ﻣﺮﺗﺒﻂ ﺑﺎ زﻣﺎن را ﻣﻨﺘﻘﻞ ﻧﮑﻨﻨﺪ، ﺑﺴﯿﺎر ﻣﻬﻢ‬
 ‫اﺳﺖ؛ ﺑﻪ ﻋﺒﺎرت دﯾﮕﺮ ﻧﻘﺎط داده ﻫﺎ ﻓﻘﻂ ﺑﺮ اﺳﺎس ﻣﻘﺎدﯾﺮﺷﺎن‬
                                           ‫رﺳﻢ ﻣﯽ ﺷﻮﻧﺪ.‬



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‫ﻧﻤﻮدارﻫﺎي ﻧﺎﺣﯿﻪ اي ﯾﺎ ﻣﺤﯿﻄﯽ‬




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        ‫ﻧﻤﻮدارﻫﺎي ﻧﺎﺣﯿﻪ اي ﯾﺎ ﻣﺤﯿﻄﯽ‬

‫• ﻫﻤﺎﻧﻨﺪ ﻧﻤﻮدار ﺧﻄﯽ ﺑﺎ اﯾﻦ ﺗﻔﺎوت ﮐﻪ ﻧﺎﺣﯿﻪ زﯾﺮ ﺧﻂ رﻧﮕﯽ ﺷﺪه‬
                                                  ‫اﺳﺖ.‬




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‫ﻧﻤﻮدارﻫﺎي دوﻧﺎت )‪(Doughnut‬‬




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      ‫ﻧﻤﻮدارﻫﺎي دوﻧﺎت )‪(Doughnut‬‬

‫• ﯾﮏ ﻧﻤﻮدار ﺣﻠﻘﻮي ﺷﺒﯿﻪ ﯾﮏ ﻧﻤﻮدار داﯾﺮه اي اﺳﺖ. اﻟﺒﺘﻪ ﺑﺎ 2‬
‫اﺳﺘﺜﻨﺎ: ﻧﻤﻮدار ﺣﻠﻘﻮي در وﺳﻂ ﺑﻪ ﺻﻮرت ﯾﮑﭙﺎرﭼﻪ اﺳﺖ و ﻣﯽ‬
               ‫ﺗﻮان ﺑﯿﺶ از ﯾﮏ ﺳﺮي داده را در آن ﻧﺸﺎن داد.‬
‫• ﺑﻬﺘﺮﯾﻦ ﮐﺎرﺑﺮد ﻧﻤﻮدار دوﻧﺎت رﺳﻢ ﯾﮏ ﺳﺮي ﻣﻨﻔﺮد ﺑﻪ ﻋﻨﻮان‬
            ‫ﺟﺎي ﮔﺰﯾﻨﯽ ﺑﺼﺮي ﺑﺮاي ﯾﮏ ﻧﻤﻮدار داﯾﺮه اي ﺑﺎﺷﺪ.‬




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‫ﻧﻤﻮدار رادار )‪(Radar‬‬




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       ‫ﻧﻤﻮدار رادار )‪(Radar‬‬

  ‫ﻧﻤﻮدار رادار داراي ﻣﺤﻮر ﻣﺠﺰاﯾﯽ ﺑﺮاي ﻫﺮ ﮔﺮوه اﺳﺖ.‬   ‫•‬
‫ﻣﺤﻮرﻫﺎ از ﻣﺮﮐﺰ ﻧﻤﻮدار ﺑﻪ ﻃﺮف ﺑﯿﺮون ﺧﺎرج ﻣﯽ ﺷﻮﻧﺪ.‬     ‫•‬
            ‫ﻣﺜﺎل: ﺑﺮاي ﻧﺸﺎن دادن ﺗﻮﺳﻌﻪ ﻫﻤﻪ ﺟﺎﻧﺒﻪ‬     ‫•‬
                 ‫ﺑﺮاي ﻧﺸﺎن دادن ﻧﻘﺎط ﻗﻮت و ﺿﻌﻒ‬       ‫•‬
  ‫ﺑﺮاي ﻧﺸﺎن دادن وﺿﻌﯿﺖ ﯾﮏ ﻣﻮﺿﻮع در 21 ﻣﺎه ﺳﺎل‬        ‫•‬




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‫ﻧﻤﻮدارﻫﺎي ﺳﻄﺤﯽ‬




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         ‫ﻧﻤﻮدارﻫﺎي ﺳﻄﺤﯽ )‪(Surface‬‬

        ‫ﯾﮏ ﯾﺎ ﭼﻨﺪ ﺳﺮي داده را در ﯾﮏ ﺳﻄﺢ ﻧﺸﺎن ﻣﯽ دﻫﺪ.‬        ‫•‬
  ‫از رﻧﮓ ﺑﺮاي ﻣﺸﺨﺺ ﮐﺮدن ﻣﻘﺎدﯾﺮ اﺳﺘﻔﺎده ﻣﯽ ﮐﻨﺪ ﻧﻪ ﺑﺮاي‬       ‫•‬
                              ‫ﻣﺸﺨﺺ ﮐﺮدن ﺳﺮي داده ﻫﺎ.‬
                     ‫ﻫﺮ رﻧﮓ ﻣﻄﺎﺑﻖ ﺑﺎ ﯾﮏ واﺣﺪ اﺻﻠﯽ اﺳﺖ.‬      ‫•‬
   ‫ﯾﮏ ﻧﻤﻮدار ﺳﻄﺤﯽ ﻧﻘﺎط داده اي ﺳﻪ ﺑﻌﺪي رﺳﻢ ﻧﻤﯽ ﮐﻨﺪ.‬         ‫•‬
 ‫اﮔﺮ داده ﻫﺎﯾﯽ دارﯾﺪ ﮐﻪ ﺑﺎ ﻣﺨﺘﺼﺎت ‪ x , y , z‬ﻧﺸﺎن داده ﺷﺪه‬   ‫•‬
‫اﻧﺪ، ﻧﻤﯽ ﺗﻮاﻧﻨﺪ ﺑﻪ ﺻﻮرت درﺳﺖ و دﻗﯿﻖ در ﯾﮏ ﻧﻤﻮدار ﺳﻄﺤﯽ‬
                                              ‫رﺳﻢ ﺷﻮﻧﺪ.‬



                                                                      ‫23‬
‫2102/72/6‬




‫ﻧﻤﻮدارﻫﺎي ﺣﺒﺎﺑﯽ )‪(Bubble‬‬




                                 ‫33‬
‫2102/72/6‬




         ‫ﻧﻤﻮدارﻫﺎي ﺣﺒﺎﺑﯽ )‪(Bubble‬‬

‫• ﯾﮏ ﻧﻤﻮدار ﺣﺒﺎﺑﯽ ﻫﻤﺎﻧﻨﺪ ﻧﻤﻮدار ‪ XY‬اﺳﺖ ﮐﻪ ﻣﯽ ﺗﻮاﻧﺪ ﯾﮑﺴﺮي‬
                                 ‫داده اﺿﺎﻓﯽ را ﻧﺸﺎن دﻫﺪ.‬
  ‫• در اﯾﻦ ﻧﻤﻮدار، ﺳﺮي داده ﻫﺎ ﺑﻪ ﺻﻮرت ﺣﺒﺎب اراﺋﻪ ﻣﯽ ﺷﻮد.‬
     ‫• ﻫﺮ دو ﻣﺤﻮر، ﻣﺤﻮر ﻣﻘﺪار اﺳﺖ و ﻣﺤﻮر ﮔﺮوه وﺟﻮد ﻧﺪارد.‬




                                                                  ‫43‬
‫2102/72/6‬




‫ﻣﺜﺎل ﻧﻤﻮدار ﺣﺒﺎﺑﯽ-ﺳﻄﺢ ﺳﻼﻣﺖ ﮐﺸﻮرﻫﺎ ﺑﻪ ﻧﺴﺒﺖ درآﻣﺪ‬




                                                        ‫53‬
‫2102/72/6‬




‫ﻧﻤﻮدار ﭘﺎرﺗﻮ )‪20-80 -(Pareto‬‬




                                     ‫63‬
‫2102/72/6‬




‫ﻧﻤﻮدار ﻧﺮﻣﺎل )‪(Norminal‬‬




                                ‫73‬
‫2102/72/6‬




                          ‫ﺗﻮزﯾﻊ ﻧﺮﻣﺎل‬
‫ﺗﻮزﯾﻊ ﻧﺮﻣﺎل ﯾﺎ ﺗﻮزﯾﻊ ﮔﻮﺳﯽ )ﯾﺎ ﮔﺎوﺳﯽ( ﯾﮑﯽ از ﺗﻮزﯾﻊﻫﺎي اﺣﺘﻤﺎﻻﺗﯽي ﭘﯿﻮﺳﺘﻪ‬
‫ﻣﻬﻢ اﺳﺖ. اﯾﻦ ﺗﻮزﯾﻊ ﺑﺎ ﺑﺮدار ﻣﯿﺎﻧﮕﯿﻦ و ﻣﺎﺗﺮﯾﺲ ﮐﻮارﯾﺎﻧﺲ آن ﺗﻮﺻﯿﻒ‬
‫ﻣﯽﺷﻮد. ﺗﻮزﯾﻊ ﻧﺮﻣﺎل اﺳﺘﺎﻧﺪاردﺗﻮزﯾﻌﯽ ﺑﺎ ﻣﯿﺎﻧﮕﯿﻦ ﺻﻔﺮ و ﻣﺎﺗﺮﯾﺲ ﮐﻮارﯾﺎﻧﺲ‬
‫واﺣﺪ اﺳﺖ )ﺧﻂ ﺳﺒﺰ ﮐﺸﯿﺪه ﺷﺪه در ﻧﻤﻮدار ﺑﺮاي ﺣﺎﻟﺖ ﺗﮏﺑﻌﺪي(. ﺑﻪ ﻋﻠﺖ‬
         ‫ﺷﺒﺎﻫﺖ اﯾﻦ ﺷﮑﻞ ﺑﻪ زﻧﮕﻮﻟﻪ ﺑﻪ آن اﻧﺤﻨﺎي زﻧﮕﻮﻟﻪاي ﻧﯿﺰ ﮔﻔﺘﻪ ﻣﯽﺷﻮد.‬
‫دﻟﯿﻞ اﻫﻤﯿﺖ ﺗﻮزﯾﻊ ﻧﺮﻣﺎل از وﺟﻮد ﻗﻀﯿﻪ ﺣﺪ ﻣﺮﮐﺰي ﻧﺎﺷﯽ ﻣﯽﺷﻮد. اﯾﻦ ﻗﻀﯿﻪ‬
‫ﻣﯽﮔﻮﯾﺪ ﮐﻪ ﻫﻨﮕﺎﻣﯽ ﮐﻪ ﺗﻌﺪاد ﺑﺴﯿﺎر زﯾﺎدي ﻣﺘﻐﯿﺮ ﺗﺼﺎدﻓﯽ ﺑﺎ ﺗﻮزﯾﻊ دلﺧﻮاه )و‬
‫اﻟﺒﺘﻪ ﺑﺎ وارﯾﺎﻧﺲ ﻣﺤﺪود( را ﺑﺎ ﻫﻢ ﺟﻤﻊ ﮐﻨﯿﻢ و ﻣﯿﺎﻧﮕﯿﻦ ﺑﮕﯿﺮﯾﻢ، ﺗﻮزﯾﻊ ﻧﻬﺎﯾﯽ ﺑﻪ‬
‫ﺗﻮزﯾﻊ ﻧﺮﻣﺎل ﻣﯿﻞ ﻣﯽﮐﻨﺪ. ﺑﻪ ﻫﻤﯿﻦ ﺧﺎﻃﺮ ﻫﻨﮕﺎﻣﯽ ﮐﻪ ﺷﺎﻫﺪ ﺗﺄﺛﯿﺮ ﺟﻤﻌﯽي‬
‫ﺑﺴﯿﺎري از ﭘﺪﯾﺪهﻫﺎي ﺗﺼﺎدﻓﯽ ﻫﺴﺘﯿﻢ، ﻧﺘﯿﺠﻪ ﻧﻬﺎﯾﯽ ﺑﺎ ﺗﻮزﯾﻊ ﻧﺮﻣﺎل ﻗﺎﺑﻞ‬
                                                           ‫ﺗﻮﺻﯿﻒ اﺳﺖ.‬
‫از ﻣﻬﻢﺗﺮﯾﻦ ﮐﺎرﺑﺮدﻫﺎي اﯾﻦ ﺗﺎﺑﻊ ﺗﻮزﯾﻊ در داﻧﺶ اﻗﺘﺼﺎد و ﻣﺪﯾﺮﯾﺖ اﻣﺮوز ﻣﯽﺗﻮان‬
‫ﺑﻪ ﻣﺪل ﮐﺮدن ﭘﻮرﺗﻔﻮﻟﯿﻮﻫﺎ ) )‪Portfolios‬در ﺳﺮﻣﺎﯾﻪ ﮔﺬاري و ﻣﺪﯾﺮﯾﺖ ﻣﻨﺎﺑﻊ‬
‫ﻧﺎم ﺑﺮد. ﻫﻨﮕﺎﻣﯽ ﮐﻪ ﻣﻘﺪار ﻣﻨﻔﯽ ﺑﺮاي ﻣﺘﻐﯿﯿﺮ ﻣﻌﻨﯽ ﻧﺪاﺷﺘﻪ ﺑﺎﺷﺪ ﻣﻌﻤﻮﻻ" در‬
‫ﻣﺤﻮر ‪x‬ﻣﻨﺤﻨﯽ را ﻣﻨﻘﻞ ﻣﯽﮐﻨﻨﺪ و ﻣﻘﺪار ﻣﯿﺎﻧﮕﯿﻦ - ﮐﻪ داراي ﺑﯿﺸﺘﺮﯾﻦ اﺣﺘﻤﺎل‬
                     ‫وﻗﻮع ﻫﺴﺖ - را ﺑﻪ ﺳﻤﺖ ﻣﻘﺎدﯾﺮ ﺑﺰﮔﺘﺮ ﺷﯿﻔﺖ ﻣﯽدﻫﻨﺪ.‬


                                                                                   ‫83‬
‫2102/72/6‬




‫ﻧﻤﻮدار ﻗﯿﻔﯽ‬




                    ‫93‬
‫2102/72/6‬




‫ﻧﻤﻮدارﻫﺎي ﻣﺨﺮوﻃﯽ و ﻫﺮﻣﯽ‬




                                ‫04‬
‫2102/72/6‬




‫ﻧﻤﻮدار ﻫﯿﺴﺘﻮﮔﺮام‬




                         ‫14‬
‫2102/72/6‬




‫ﻧﻤﻮدار ﮔﺎﻧﺖ )‪(Gantt‬‬




                            ‫24‬
‫2102/72/6‬




‫ﻧﻤﻮدار ﺟﺮﯾﺎن ﻧﻘﺪي )‪(Cash Flow‬‬




                                      ‫34‬
‫2102/72/6‬




‫ﻧﻤﻮدار اﺳﺘﺨﻮان ﻣﺎﻫﯽ ﯾﺎ ﻋﻠﺖ و ﻣﻌﻠﻮﻟﯽ )‪(Fishbone‬‬




                                                       ‫44‬
‫2102/72/6‬




‫ﻧﻤﻮدار ﺧﻂ زﻣﺎن )‪(Timeline‬‬




                                  ‫54‬

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Chart&diagram- انواع نمودار و کاربرد آن

  • 1. ‫2102/72/6‬ ‫ﻣﻌﺮﻓﯽ و آﻣﻮزش اﻧﻮاع ﻧﻤﻮدار‬ ‫‪Chart & Diagram Training‬‬ ‫اراﺋﻪ دﻫﻨﺪه: ﮐﯿﻮان ﺟﻌﻔﺮي ﻓﺸﺎرﮐﯽ‬ ‫اﻧﺪﯾﺸﮑﺪه ﮐﯿﻮان‬ ‫‪www.k1j.ir‬‬ ‫وﺑﮕﺎه:‬ ‫‪k1j@k1j.ir‬‬ ‫ﭘﺴﺖ اﻟﮑﺘﺮوﻧﯿﮏ:‬ ‫1‬ ‫1‬
  • 2. ‫2102/72/6‬ ‫ﺑﻪ ﻧﺎم ﯾﮕﺎﻧﻪ ي داﻧﺎ و ﺗﻮاﻧﺎ‬ ‫2‬ ‫2‬
  • 3. ‫2102/72/6‬ ‫ﻣﻘﺪﻣﻪ‬ ‫ﻣﻔﺎﻫﯿﻢ ﭘﺎﯾﻪ‬ ‫اﻫﺪاف ﺗﺮﺳﯿﻢ ﻧﻤﻮدار‬ ‫اﺳﺘﺎﻧﺪاردﻫﺎ و ﻗﻮاﻧﯿﻦ رﺳﻢ ﻧﻤﻮدار‬ ‫1- اﻧﻮاع ﻧﻤﻮدار‬ ‫ﺳﺘﻮﻧﯽ‬ ‫ﺧﻄﯽ‬ ‫داﯾﺮه اي‬ ‫2- ﺗﺮﺳﯿﻢ ﻧﻤﻮدارﻫﺎي ﻣﺨﺘﻠﻒ در ﻧﺮم اﻓﺰار اﮐﺴﻞ‬ ‫3- ﺗﺮﺳﯿﻢ ﻧﻤﻮدار در ﻧﺮم اﻓﺰارﻫﺎي دﯾﮕﺮ‬ ‫3‬ ‫3‬
  • 4. ‫2102/72/6‬ ‫اﻧﺘﻘﺎل ﭘﯿﺎم ﺑﺎ ﯾﮏ ﻧﻤﻮدار‬ ‫ﻣﻘﺎﯾﺴﻪ آﯾﺘﻤﯽ ﺑﺎ آﯾﺘﻤﯽ دﯾﮕﺮ‬ ‫•‬ ‫ﻣﻘﺎﯾﺴﻪ داده ﻫﺎ ﺑﺮ اﺳﺎس زﻣﺎن‬ ‫•‬ ‫ﻣﻘﺎﯾﺴﺎت ﻧﺴﺒﯽ )ﻣﺎﻧﻨﺪ ﻧﻤﻮدار ﻫﺎي داﯾﺮه اي(‬ ‫•‬ ‫ﻣﻘﺎﯾﺴﻪ رواﺑﻂ داده اي )ﻣﺎﻧﻨﺪ ﻧﻤﻮدار ‪(XY‬‬ ‫•‬ ‫ﻣﻘﺎﯾﺴﻪ ﺑﺴﺎﻣﺪي‬ ‫•‬ ‫ﻣﺸﺨﺺ ﮐﺮدن “داده ﭘﺮاﮐﻨﺪه” ﯾﺎ ﻣﻮﻗﻌﯿﺖ ﻫﺎ ﻏﯿﺮ ﻣﻌﻤﻮل‬ ‫•‬ ‫4‬
  • 5. ‫2102/72/6‬ ‫اﻧﺘﺨﺎب ﻧﻮع ﻧﻤﻮدار‬ ‫• از ﻧﻤﻮداري اﺳﺘﻔﺎده ﮐﻨﯿﺪ ﮐﻪ ﭘﯿﺎم ﺷﻤﺎ را ﺑﻪ ﺳﺎده ﺗﺮﯾﻦ و دﻗﯿﻖ‬ ‫ﺗﺮﯾﻦ ﺷﮑﻞ ﻣﻤﮑﻦ ﺑﯿﺎن ﮐﻨﺪ.‬ ‫5‬
  • 6. ‫2102/72/6‬ ‫ﺗﻌﺮﯾﻒ ﻧﻤﻮدار-اﻧﻮاع ﻧﻤﻮدار‬ ‫ﺑﻪ ﻧﻤﺎﯾﺶ ﺑﺼﺮي ﻣﻔﺎﻫﯿﻢ، اﯾﺪه ﻫﺎ، ﺳﺎﺧﺘﺎرﻫﺎ، رواﺑﻂ، دادهﻫﺎي آﻣﺎري و ﻏﯿﺮه ﺑﻪ‬ ‫ﮔﻮﻧﻪاي ﺳﺎده و ﺷﮑﻞ ﯾﺎﻓﺘﻪ ﻧﻤﻮدار ﻣﯽﮔﻮﯾﻨﺪ. از ﻧﻤﻮدارﻫﺎ ﺑﺮاي ﺳﺎده ﮐﺮدن و‬ ‫ﻣﻠﻤﻮس ﮐﺮدن ﻣﻮﺿﻮﻋﺎت ﮔﻮﻧﺎﮔﻮن اﺳﺘﻔﺎده ﻣﯽﺷﻮد.‬ ‫ﺳﻄﺤﯽ‬ ‫ﺳﺘﻮﻧﯽ: ﺳﺘﻮﻧﯽ 2 ﺑﻌﺪي، ﺳﺘﻮﻧﯽ 3‬ ‫داﮔﻨﺎت‬ ‫ﺑﻌﺪي، ﻣﯿﻠﻪ اي، ﻣﺨﺮوﻃﯽ، ﻫﺮﻣﯽ‬ ‫ﺣﺒﺎﺑﯽ، ﺗﻮﭘﯽ‬ ‫ﺧﻄﯽ)روﻧﺪ(: ﺧﻄﯽ 2 ﺑﻌﺪي، ﺧﻄﯽ‬ ‫رادار‬ ‫3 ﺑﻌﺪي‬ ‫ﻓﺼﻠﯽ‬ ‫ﭘﺎي: ﭘﺎي 2 ﺑﻌﺪي، ﭘﺎي 3 ﺑﻌﺪي‬ ‫ﻧﺮﻣﺎل‬ ‫ﻧﻮاري)ﺑﺎر(: ﻧﻮاري 2 ﺑﻌﺪي، ﻧﻮاري‬ ‫ﺧﻂ زﻣﺎن‬ ‫3 ﺑﻌﺪي، ﻣﯿﻠﻪ اي، ﻣﺨﺮوﻃﯽ، ﻫﺮﻣﯽ‬ ‫اﺳﺘﺨﻮان ﻣﺎﻫﯽ‬ ‫ﻣﺤﯿﻄﯽ: 2 ﺑﻌﺪي، 3 ﺑﻌﺪي‬ ‫ﮔﺎﻧﺖ‬ ‫ﭘﺮاﮐﻨﺪﮔﯽ )‪ :(X-Y‬ﻧﻘﻄﻪ اي،‬ ‫ﺟﺮﯾﺎن ﻧﻘﺪي‬ ‫ﺳﻬﺎﻣﯽ‬ ‫6‬
  • 13. ‫2102/72/6‬ ‫ﻧﻤﻮدارﻫﺎي ﺳﺘﻮﻧﯽ )‪(Column‬‬ ‫• ﻫﺮ ﯾﮏ از ﻧﻘﺎط داده اي را ﺑﻪ ﺻﻮرت ﯾﮏ ﺳﺘﻮن ﻋﻤﻮدي ﻧﺸﺎن‬ ‫ﻣﯽ دﻫﺪ. ارﺗﻔﺎع ﻧﻤﺎﯾﺎﻧﮕﺮ ﻣﻘﺪار ﻣﯽ ﺑﺎﺷﺪ.‬ ‫• ﻧﻘﺎط داده اي ﻣﺮﺑﻮط ﺑﻪ ﻫﺮ ﺳﺮي از داده ﻣﯽ ﺗﻮاﻧﻨﺪ ﺑﺮ روي‬ ‫ﻫﻤﺪﯾﮕﺮ ﭘﺸﺘﻪ ﺷﻮﻧﺪ.‬ ‫• اﻏﻠﺐ ﺟﻬﺖ ﻣﻘﺎﯾﺴﻪ آﯾﺘﻢ ﻫﺎي ﻣﺠﺰا ﺑﻪ ﮐﺎر ﻣﯽ روﻧﺪ و ﻣﯽ ﺗﻮاﻧﻨﺪ‬ ‫ﺗﻔﺎوت ﻫﺎي ﻣﻮﺟﻮد ﺑﯿﻦ آﯾﺘﻢ ﻫﺎي ﯾﮑﺴﺮي و ﯾﺎ ﺳﺮي ﻫﺎي‬ ‫ﭼﻨﺪﮔﺎﻧﻪ را ﻧﺸﺎن دﻫﻨﺪ.‬ ‫31‬
  • 15. ‫2102/72/6‬ ‫ﻧﻤﻮدارﻫﺎي ﻣﯿﻠﻪ اي )‪(Bar‬‬ ‫• ﺷﺒﯿﻪ ﻧﻤﻮدار ﺳﺘﻮﻧﯽ اﺳﺖ ﮐﻪ 09 درﺟﻪ در ﺟﻬﺖ ﻋﻘﺮﺑﻪ ﻫﺎي‬ ‫ﺳﺎﻋﺖ ﭼﺮﺧﯿﺪه اﺳﺖ.‬ ‫• ﻣﺰﯾﺖ آن ﺧﻮاﻧﺪن آﺳﺎن ﺗﺮ ﻋﻨﺎوﯾﻦ و ﺑﺮﭼﺴﺐ ﻫﺎي ﻫﺮ ﮔﺮوه ﻣﯽ‬ ‫ﺑﺎﺷﺪ.‬ ‫• ﺑﺮﺧﻼف ﻧﻤﻮدار ﺳﺘﻮﻧﯽ، در ﻧﻤﻮدار ﻣﯿﻠﻪ اي ﻫﯿﭻ ﻧﻤﻮدار ﻓﺮﻋﯽ ﮐﻪ‬ ‫ﻫﻤﺮاه ﺑﺎ ﻣﺤﻮر ﺳﻮم ﭼﻨﺪﯾﻦ ﺳﺮي را ﻧﻤﺎﯾﺶ دﻫﺪ، ﻣﻮﺟﻮد ﻧﻤﯽ‬ ‫ﺑﺎﺷﺪ. )ﻫﯿﭻ ﻧﻮع ﻧﻤﻮدار ﻓﺮﻋﯽ ‪ 3D-Bar Chart‬وﺟﻮد ﻧﺪارد.‬ ‫51‬
  • 17. ‫2102/72/6‬ ‫ﻧﻤﻮدارﻫﺎي ﺧﻄﯽ‬ ‫• اﻏﻠﺐ ﺑﺮاي رﺳﻢ داده ﻫﺎي ﭘﯿﻮﺳﺘﻪ ﺑﻪ ﮐﺎر ﻣﯽ رود‬ ‫• ﺑﺮاي ﺗﻌﯿﯿﻦ ﺟﻬﺖ و ﮔﺮاﯾﺶ ﻣﻔﯿﺪ اﺳﺖ‬ ‫• ﺗﺮﺳﯿﻢ ﻓﺮوش ﻣﺎﻫﯿﺎﻧﻪ‬ ‫71‬
  • 18. ‫2102/72/6‬ ‫ﻧﻤﻮدار ﻣﻘﺎﯾﺴﻪ اي ﺳﺎل ﻫﺎ-ﻓﺼﻞ ﻫﺎ و ﻣﺎه ﻫﺎ‬ ‫81‬
  • 19. ‫2102/72/6‬ ‫ﻣﻘﺎﯾﺴﻪ روﻧﺪﻫﺎي ﭼﻨﺪ ﺳﺎل ﻗﯿﻤﺖ ﻃﻼ‬ ‫91‬
  • 22. ‫2102/72/6‬ ‫ﻧﻤﻮدارﻫﺎي داﯾﺮه اي )‪(Pie‬‬ ‫ﺑﺮاي ﻧﻤﺎﯾﺶ ﺳﻬﻢ ﯾﺎ اﺑﻌﺎد ﻧﺴﺒﯽ از ﮐﻞ اﺳﺘﻔﺎده ﻣﯽ ﺷﻮد.‬ ‫•‬ ‫ﻓﻘﻂ ﻣﯽ ﺗﻮان از ﯾﮏ ﺳﺮي داده اﺳﺘﻔﺎده ﮐﺮد.‬ ‫•‬ ‫ﺑﺮاي ﻧﻘﺎط داده اي ﮐﻮﭼﮏ ﻣﻮﺛﺮﺗﺮ ﻫﺴﺘﻨﺪ.‬ ‫•‬ ‫ﻧﺒﺎﯾﺪ ﺑﯿﺶ از 5 ﯾﺎ 6 ﻧﻘﻄﻪ ي داده اي اﺳﺘﻔﺎده ﮐﺮد.‬ ‫•‬ ‫ﺑﺎﯾﺪ ﺗﻤﺎم ﻣﻘﺎدﯾﺮ اﻋﺪاد ﻣﺜﺒﺖ ﺑﺎﺷﻨﺪ.‬ ‫•‬ ‫22‬
  • 24. ‫2102/72/6‬ ‫ﻧﻤﻮدارﻫﺎي ﻣﺨﺘﺼﺎﺗﯽ ﯾﺎ ﭘﺮاﮐﻨﺪﮔﯽ )‪(XY‬‬ ‫ﻫﺮ دو ﻣﺤﻮر ﻧﺸﺎن دﻫﻨﺪه ﻣﻘﺪار ﻫﺴﺘﻨﺪ‬ ‫•‬ ‫ﺑﺮاي ﻧﺸﺎن دادن رواﺑﻂ ﺑﯿﻦ دو ﻣﺘﻐﯿﯿﺮ ﺑﻪ ﮐﺎر ﻣﯽ رود‬ ‫•‬ ‫ﻣﺜﺎل: رواﺑﻂ ﺑﯿﻦ ﻓﺮوش )ﻣﺤﻮر اﻓﻘﯽ( . ﻓﺮوش واﻗﻌﯽ )ﻣﺤﻮر‬ ‫•‬ ‫ﻋﻤﻮدي(‬ ‫ﺗﻮﺟﻪ: ﺑﺎ اﯾﻨﮑﻪ ﻧﻘﺎط داده ﻫﺎ ﻣﻄﺎﺑﻖ ﺑﺎ زﻣﺎن اﺳﺖ، اﻣﺎ درك اﯾﻦ‬ ‫•‬ ‫ﻣﻄﻠﺐ ﮐﻪ اﻃﻼﻋﺎت ﻣﺮﺗﺒﻂ ﺑﺎ زﻣﺎن را ﻣﻨﺘﻘﻞ ﻧﮑﻨﻨﺪ، ﺑﺴﯿﺎر ﻣﻬﻢ‬ ‫اﺳﺖ؛ ﺑﻪ ﻋﺒﺎرت دﯾﮕﺮ ﻧﻘﺎط داده ﻫﺎ ﻓﻘﻂ ﺑﺮ اﺳﺎس ﻣﻘﺎدﯾﺮﺷﺎن‬ ‫رﺳﻢ ﻣﯽ ﺷﻮﻧﺪ.‬ ‫42‬
  • 26. ‫2102/72/6‬ ‫ﻧﻤﻮدارﻫﺎي ﻧﺎﺣﯿﻪ اي ﯾﺎ ﻣﺤﯿﻄﯽ‬ ‫• ﻫﻤﺎﻧﻨﺪ ﻧﻤﻮدار ﺧﻄﯽ ﺑﺎ اﯾﻦ ﺗﻔﺎوت ﮐﻪ ﻧﺎﺣﯿﻪ زﯾﺮ ﺧﻂ رﻧﮕﯽ ﺷﺪه‬ ‫اﺳﺖ.‬ ‫62‬
  • 28. ‫2102/72/6‬ ‫ﻧﻤﻮدارﻫﺎي دوﻧﺎت )‪(Doughnut‬‬ ‫• ﯾﮏ ﻧﻤﻮدار ﺣﻠﻘﻮي ﺷﺒﯿﻪ ﯾﮏ ﻧﻤﻮدار داﯾﺮه اي اﺳﺖ. اﻟﺒﺘﻪ ﺑﺎ 2‬ ‫اﺳﺘﺜﻨﺎ: ﻧﻤﻮدار ﺣﻠﻘﻮي در وﺳﻂ ﺑﻪ ﺻﻮرت ﯾﮑﭙﺎرﭼﻪ اﺳﺖ و ﻣﯽ‬ ‫ﺗﻮان ﺑﯿﺶ از ﯾﮏ ﺳﺮي داده را در آن ﻧﺸﺎن داد.‬ ‫• ﺑﻬﺘﺮﯾﻦ ﮐﺎرﺑﺮد ﻧﻤﻮدار دوﻧﺎت رﺳﻢ ﯾﮏ ﺳﺮي ﻣﻨﻔﺮد ﺑﻪ ﻋﻨﻮان‬ ‫ﺟﺎي ﮔﺰﯾﻨﯽ ﺑﺼﺮي ﺑﺮاي ﯾﮏ ﻧﻤﻮدار داﯾﺮه اي ﺑﺎﺷﺪ.‬ ‫82‬
  • 30. ‫2102/72/6‬ ‫ﻧﻤﻮدار رادار )‪(Radar‬‬ ‫ﻧﻤﻮدار رادار داراي ﻣﺤﻮر ﻣﺠﺰاﯾﯽ ﺑﺮاي ﻫﺮ ﮔﺮوه اﺳﺖ.‬ ‫•‬ ‫ﻣﺤﻮرﻫﺎ از ﻣﺮﮐﺰ ﻧﻤﻮدار ﺑﻪ ﻃﺮف ﺑﯿﺮون ﺧﺎرج ﻣﯽ ﺷﻮﻧﺪ.‬ ‫•‬ ‫ﻣﺜﺎل: ﺑﺮاي ﻧﺸﺎن دادن ﺗﻮﺳﻌﻪ ﻫﻤﻪ ﺟﺎﻧﺒﻪ‬ ‫•‬ ‫ﺑﺮاي ﻧﺸﺎن دادن ﻧﻘﺎط ﻗﻮت و ﺿﻌﻒ‬ ‫•‬ ‫ﺑﺮاي ﻧﺸﺎن دادن وﺿﻌﯿﺖ ﯾﮏ ﻣﻮﺿﻮع در 21 ﻣﺎه ﺳﺎل‬ ‫•‬ ‫03‬
  • 32. ‫2102/72/6‬ ‫ﻧﻤﻮدارﻫﺎي ﺳﻄﺤﯽ )‪(Surface‬‬ ‫ﯾﮏ ﯾﺎ ﭼﻨﺪ ﺳﺮي داده را در ﯾﮏ ﺳﻄﺢ ﻧﺸﺎن ﻣﯽ دﻫﺪ.‬ ‫•‬ ‫از رﻧﮓ ﺑﺮاي ﻣﺸﺨﺺ ﮐﺮدن ﻣﻘﺎدﯾﺮ اﺳﺘﻔﺎده ﻣﯽ ﮐﻨﺪ ﻧﻪ ﺑﺮاي‬ ‫•‬ ‫ﻣﺸﺨﺺ ﮐﺮدن ﺳﺮي داده ﻫﺎ.‬ ‫ﻫﺮ رﻧﮓ ﻣﻄﺎﺑﻖ ﺑﺎ ﯾﮏ واﺣﺪ اﺻﻠﯽ اﺳﺖ.‬ ‫•‬ ‫ﯾﮏ ﻧﻤﻮدار ﺳﻄﺤﯽ ﻧﻘﺎط داده اي ﺳﻪ ﺑﻌﺪي رﺳﻢ ﻧﻤﯽ ﮐﻨﺪ.‬ ‫•‬ ‫اﮔﺮ داده ﻫﺎﯾﯽ دارﯾﺪ ﮐﻪ ﺑﺎ ﻣﺨﺘﺼﺎت ‪ x , y , z‬ﻧﺸﺎن داده ﺷﺪه‬ ‫•‬ ‫اﻧﺪ، ﻧﻤﯽ ﺗﻮاﻧﻨﺪ ﺑﻪ ﺻﻮرت درﺳﺖ و دﻗﯿﻖ در ﯾﮏ ﻧﻤﻮدار ﺳﻄﺤﯽ‬ ‫رﺳﻢ ﺷﻮﻧﺪ.‬ ‫23‬
  • 34. ‫2102/72/6‬ ‫ﻧﻤﻮدارﻫﺎي ﺣﺒﺎﺑﯽ )‪(Bubble‬‬ ‫• ﯾﮏ ﻧﻤﻮدار ﺣﺒﺎﺑﯽ ﻫﻤﺎﻧﻨﺪ ﻧﻤﻮدار ‪ XY‬اﺳﺖ ﮐﻪ ﻣﯽ ﺗﻮاﻧﺪ ﯾﮑﺴﺮي‬ ‫داده اﺿﺎﻓﯽ را ﻧﺸﺎن دﻫﺪ.‬ ‫• در اﯾﻦ ﻧﻤﻮدار، ﺳﺮي داده ﻫﺎ ﺑﻪ ﺻﻮرت ﺣﺒﺎب اراﺋﻪ ﻣﯽ ﺷﻮد.‬ ‫• ﻫﺮ دو ﻣﺤﻮر، ﻣﺤﻮر ﻣﻘﺪار اﺳﺖ و ﻣﺤﻮر ﮔﺮوه وﺟﻮد ﻧﺪارد.‬ ‫43‬
  • 35. ‫2102/72/6‬ ‫ﻣﺜﺎل ﻧﻤﻮدار ﺣﺒﺎﺑﯽ-ﺳﻄﺢ ﺳﻼﻣﺖ ﮐﺸﻮرﻫﺎ ﺑﻪ ﻧﺴﺒﺖ درآﻣﺪ‬ ‫53‬
  • 38. ‫2102/72/6‬ ‫ﺗﻮزﯾﻊ ﻧﺮﻣﺎل‬ ‫ﺗﻮزﯾﻊ ﻧﺮﻣﺎل ﯾﺎ ﺗﻮزﯾﻊ ﮔﻮﺳﯽ )ﯾﺎ ﮔﺎوﺳﯽ( ﯾﮑﯽ از ﺗﻮزﯾﻊﻫﺎي اﺣﺘﻤﺎﻻﺗﯽي ﭘﯿﻮﺳﺘﻪ‬ ‫ﻣﻬﻢ اﺳﺖ. اﯾﻦ ﺗﻮزﯾﻊ ﺑﺎ ﺑﺮدار ﻣﯿﺎﻧﮕﯿﻦ و ﻣﺎﺗﺮﯾﺲ ﮐﻮارﯾﺎﻧﺲ آن ﺗﻮﺻﯿﻒ‬ ‫ﻣﯽﺷﻮد. ﺗﻮزﯾﻊ ﻧﺮﻣﺎل اﺳﺘﺎﻧﺪاردﺗﻮزﯾﻌﯽ ﺑﺎ ﻣﯿﺎﻧﮕﯿﻦ ﺻﻔﺮ و ﻣﺎﺗﺮﯾﺲ ﮐﻮارﯾﺎﻧﺲ‬ ‫واﺣﺪ اﺳﺖ )ﺧﻂ ﺳﺒﺰ ﮐﺸﯿﺪه ﺷﺪه در ﻧﻤﻮدار ﺑﺮاي ﺣﺎﻟﺖ ﺗﮏﺑﻌﺪي(. ﺑﻪ ﻋﻠﺖ‬ ‫ﺷﺒﺎﻫﺖ اﯾﻦ ﺷﮑﻞ ﺑﻪ زﻧﮕﻮﻟﻪ ﺑﻪ آن اﻧﺤﻨﺎي زﻧﮕﻮﻟﻪاي ﻧﯿﺰ ﮔﻔﺘﻪ ﻣﯽﺷﻮد.‬ ‫دﻟﯿﻞ اﻫﻤﯿﺖ ﺗﻮزﯾﻊ ﻧﺮﻣﺎل از وﺟﻮد ﻗﻀﯿﻪ ﺣﺪ ﻣﺮﮐﺰي ﻧﺎﺷﯽ ﻣﯽﺷﻮد. اﯾﻦ ﻗﻀﯿﻪ‬ ‫ﻣﯽﮔﻮﯾﺪ ﮐﻪ ﻫﻨﮕﺎﻣﯽ ﮐﻪ ﺗﻌﺪاد ﺑﺴﯿﺎر زﯾﺎدي ﻣﺘﻐﯿﺮ ﺗﺼﺎدﻓﯽ ﺑﺎ ﺗﻮزﯾﻊ دلﺧﻮاه )و‬ ‫اﻟﺒﺘﻪ ﺑﺎ وارﯾﺎﻧﺲ ﻣﺤﺪود( را ﺑﺎ ﻫﻢ ﺟﻤﻊ ﮐﻨﯿﻢ و ﻣﯿﺎﻧﮕﯿﻦ ﺑﮕﯿﺮﯾﻢ، ﺗﻮزﯾﻊ ﻧﻬﺎﯾﯽ ﺑﻪ‬ ‫ﺗﻮزﯾﻊ ﻧﺮﻣﺎل ﻣﯿﻞ ﻣﯽﮐﻨﺪ. ﺑﻪ ﻫﻤﯿﻦ ﺧﺎﻃﺮ ﻫﻨﮕﺎﻣﯽ ﮐﻪ ﺷﺎﻫﺪ ﺗﺄﺛﯿﺮ ﺟﻤﻌﯽي‬ ‫ﺑﺴﯿﺎري از ﭘﺪﯾﺪهﻫﺎي ﺗﺼﺎدﻓﯽ ﻫﺴﺘﯿﻢ، ﻧﺘﯿﺠﻪ ﻧﻬﺎﯾﯽ ﺑﺎ ﺗﻮزﯾﻊ ﻧﺮﻣﺎل ﻗﺎﺑﻞ‬ ‫ﺗﻮﺻﯿﻒ اﺳﺖ.‬ ‫از ﻣﻬﻢﺗﺮﯾﻦ ﮐﺎرﺑﺮدﻫﺎي اﯾﻦ ﺗﺎﺑﻊ ﺗﻮزﯾﻊ در داﻧﺶ اﻗﺘﺼﺎد و ﻣﺪﯾﺮﯾﺖ اﻣﺮوز ﻣﯽﺗﻮان‬ ‫ﺑﻪ ﻣﺪل ﮐﺮدن ﭘﻮرﺗﻔﻮﻟﯿﻮﻫﺎ ) )‪Portfolios‬در ﺳﺮﻣﺎﯾﻪ ﮔﺬاري و ﻣﺪﯾﺮﯾﺖ ﻣﻨﺎﺑﻊ‬ ‫ﻧﺎم ﺑﺮد. ﻫﻨﮕﺎﻣﯽ ﮐﻪ ﻣﻘﺪار ﻣﻨﻔﯽ ﺑﺮاي ﻣﺘﻐﯿﯿﺮ ﻣﻌﻨﯽ ﻧﺪاﺷﺘﻪ ﺑﺎﺷﺪ ﻣﻌﻤﻮﻻ" در‬ ‫ﻣﺤﻮر ‪x‬ﻣﻨﺤﻨﯽ را ﻣﻨﻘﻞ ﻣﯽﮐﻨﻨﺪ و ﻣﻘﺪار ﻣﯿﺎﻧﮕﯿﻦ - ﮐﻪ داراي ﺑﯿﺸﺘﺮﯾﻦ اﺣﺘﻤﺎل‬ ‫وﻗﻮع ﻫﺴﺖ - را ﺑﻪ ﺳﻤﺖ ﻣﻘﺎدﯾﺮ ﺑﺰﮔﺘﺮ ﺷﯿﻔﺖ ﻣﯽدﻫﻨﺪ.‬ ‫83‬
  • 44. ‫2102/72/6‬ ‫ﻧﻤﻮدار اﺳﺘﺨﻮان ﻣﺎﻫﯽ ﯾﺎ ﻋﻠﺖ و ﻣﻌﻠﻮﻟﯽ )‪(Fishbone‬‬ ‫44‬