Take single element of a list, and compare to average of whole list












2














If I have a list



lst = {1,2,3,4,5};


Is there someway of taking the first element and then comparing it to the average of the other 4? Then to take element 2 and compare it to the average of element 1,3,4,5? I can see how to do this with a For loop and a procedural style, but I am wondering if an easy functional style solution is possible.



Similar to This:



 1 == Mean[{2,3,4,5}]
2 == Mean[{1,3,4,5}]
3 == Mean[{1,2,4,5}]


PS. I plan on using a more elaborate comparison, but == seemed like an easy one for this example.










share|improve this question



























    2














    If I have a list



    lst = {1,2,3,4,5};


    Is there someway of taking the first element and then comparing it to the average of the other 4? Then to take element 2 and compare it to the average of element 1,3,4,5? I can see how to do this with a For loop and a procedural style, but I am wondering if an easy functional style solution is possible.



    Similar to This:



     1 == Mean[{2,3,4,5}]
    2 == Mean[{1,3,4,5}]
    3 == Mean[{1,2,4,5}]


    PS. I plan on using a more elaborate comparison, but == seemed like an easy one for this example.










    share|improve this question

























      2












      2








      2







      If I have a list



      lst = {1,2,3,4,5};


      Is there someway of taking the first element and then comparing it to the average of the other 4? Then to take element 2 and compare it to the average of element 1,3,4,5? I can see how to do this with a For loop and a procedural style, but I am wondering if an easy functional style solution is possible.



      Similar to This:



       1 == Mean[{2,3,4,5}]
      2 == Mean[{1,3,4,5}]
      3 == Mean[{1,2,4,5}]


      PS. I plan on using a more elaborate comparison, but == seemed like an easy one for this example.










      share|improve this question













      If I have a list



      lst = {1,2,3,4,5};


      Is there someway of taking the first element and then comparing it to the average of the other 4? Then to take element 2 and compare it to the average of element 1,3,4,5? I can see how to do this with a For loop and a procedural style, but I am wondering if an easy functional style solution is possible.



      Similar to This:



       1 == Mean[{2,3,4,5}]
      2 == Mean[{1,3,4,5}]
      3 == Mean[{1,2,4,5}]


      PS. I plan on using a more elaborate comparison, but == seemed like an easy one for this example.







      list-manipulation functional-style averages






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 2 hours ago









      olliepower

      1,21511127




      1,21511127






















          2 Answers
          2






          active

          oldest

          votes


















          2














          if you want to choose a specific element use



          F[x_] := Mean@Complement[lst, {x}]
          1 == F[1]
          2 == F[2]
          3 == F[3]



          False

          False

          True




          Note



          if you want to choose the first,second,nth element use



          F[x_] := Mean@Complement[lst, {lst[[x]]}]    
          1 == F[1]
          2 == F[2]
          3 == F[3]



          False

          False

          True







          share|improve this answer































            0














            ClearAll[subMeans]
            subMeans = (Total[#] - #)/(Length[#] - 1) &;


            Examples:



            lst = {a, b, c, d};
            subMeans[lst]



            {1/3 (b + c + d), 1/3 (a + c + d), 1/3 (a + b + d), 1/3 (a + b + c)}




            MapThread[Equal, {#, subMeans @ #}]& @ lst



            {a == 1/3 (b + c + d), b == 1/3 (a + c + d), c == 1/3 (a + b + d),
            d == 1/3 (a + b + c)}




            MapThread[Equal, {#, subMeans @ #}]& @ Range[5]



            {False, False, True, False, False}







            share|improve this answer























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              2 Answers
              2






              active

              oldest

              votes








              2 Answers
              2






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes









              2














              if you want to choose a specific element use



              F[x_] := Mean@Complement[lst, {x}]
              1 == F[1]
              2 == F[2]
              3 == F[3]



              False

              False

              True




              Note



              if you want to choose the first,second,nth element use



              F[x_] := Mean@Complement[lst, {lst[[x]]}]    
              1 == F[1]
              2 == F[2]
              3 == F[3]



              False

              False

              True







              share|improve this answer




























                2














                if you want to choose a specific element use



                F[x_] := Mean@Complement[lst, {x}]
                1 == F[1]
                2 == F[2]
                3 == F[3]



                False

                False

                True




                Note



                if you want to choose the first,second,nth element use



                F[x_] := Mean@Complement[lst, {lst[[x]]}]    
                1 == F[1]
                2 == F[2]
                3 == F[3]



                False

                False

                True







                share|improve this answer


























                  2












                  2








                  2






                  if you want to choose a specific element use



                  F[x_] := Mean@Complement[lst, {x}]
                  1 == F[1]
                  2 == F[2]
                  3 == F[3]



                  False

                  False

                  True




                  Note



                  if you want to choose the first,second,nth element use



                  F[x_] := Mean@Complement[lst, {lst[[x]]}]    
                  1 == F[1]
                  2 == F[2]
                  3 == F[3]



                  False

                  False

                  True







                  share|improve this answer














                  if you want to choose a specific element use



                  F[x_] := Mean@Complement[lst, {x}]
                  1 == F[1]
                  2 == F[2]
                  3 == F[3]



                  False

                  False

                  True




                  Note



                  if you want to choose the first,second,nth element use



                  F[x_] := Mean@Complement[lst, {lst[[x]]}]    
                  1 == F[1]
                  2 == F[2]
                  3 == F[3]



                  False

                  False

                  True








                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited 2 hours ago

























                  answered 2 hours ago









                  J42161217

                  3,732220




                  3,732220























                      0














                      ClearAll[subMeans]
                      subMeans = (Total[#] - #)/(Length[#] - 1) &;


                      Examples:



                      lst = {a, b, c, d};
                      subMeans[lst]



                      {1/3 (b + c + d), 1/3 (a + c + d), 1/3 (a + b + d), 1/3 (a + b + c)}




                      MapThread[Equal, {#, subMeans @ #}]& @ lst



                      {a == 1/3 (b + c + d), b == 1/3 (a + c + d), c == 1/3 (a + b + d),
                      d == 1/3 (a + b + c)}




                      MapThread[Equal, {#, subMeans @ #}]& @ Range[5]



                      {False, False, True, False, False}







                      share|improve this answer




























                        0














                        ClearAll[subMeans]
                        subMeans = (Total[#] - #)/(Length[#] - 1) &;


                        Examples:



                        lst = {a, b, c, d};
                        subMeans[lst]



                        {1/3 (b + c + d), 1/3 (a + c + d), 1/3 (a + b + d), 1/3 (a + b + c)}




                        MapThread[Equal, {#, subMeans @ #}]& @ lst



                        {a == 1/3 (b + c + d), b == 1/3 (a + c + d), c == 1/3 (a + b + d),
                        d == 1/3 (a + b + c)}




                        MapThread[Equal, {#, subMeans @ #}]& @ Range[5]



                        {False, False, True, False, False}







                        share|improve this answer


























                          0












                          0








                          0






                          ClearAll[subMeans]
                          subMeans = (Total[#] - #)/(Length[#] - 1) &;


                          Examples:



                          lst = {a, b, c, d};
                          subMeans[lst]



                          {1/3 (b + c + d), 1/3 (a + c + d), 1/3 (a + b + d), 1/3 (a + b + c)}




                          MapThread[Equal, {#, subMeans @ #}]& @ lst



                          {a == 1/3 (b + c + d), b == 1/3 (a + c + d), c == 1/3 (a + b + d),
                          d == 1/3 (a + b + c)}




                          MapThread[Equal, {#, subMeans @ #}]& @ Range[5]



                          {False, False, True, False, False}







                          share|improve this answer














                          ClearAll[subMeans]
                          subMeans = (Total[#] - #)/(Length[#] - 1) &;


                          Examples:



                          lst = {a, b, c, d};
                          subMeans[lst]



                          {1/3 (b + c + d), 1/3 (a + c + d), 1/3 (a + b + d), 1/3 (a + b + c)}




                          MapThread[Equal, {#, subMeans @ #}]& @ lst



                          {a == 1/3 (b + c + d), b == 1/3 (a + c + d), c == 1/3 (a + b + d),
                          d == 1/3 (a + b + c)}




                          MapThread[Equal, {#, subMeans @ #}]& @ Range[5]



                          {False, False, True, False, False}








                          share|improve this answer














                          share|improve this answer



                          share|improve this answer








                          edited 46 mins ago

























                          answered 53 mins ago









                          kglr

                          177k9198405




                          177k9198405






























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