A set having the same mean, median, mode, and range












1












$begingroup$


Is it possible to have a set with the same mean, median, mode, and range?



If not, how can the following question be solved:




Set $H$ contains five positive integers such that the mean, median,
mode, and range are all equal. The sum of the data is $25$.



Using the above information, indicate which one will be greater:



a) the smallest possible number in set $H$.



b) 6.




If I assume that all the elements in set $H$ are equal to $5$, it doesn't satisfy the conditions for range, as the range will become zero then.






statistics means median







share|cite|improve this question











$endgroup$












  • $begingroup$
    The list ${0,0}$ works quite well for you first question.
    $endgroup$
    – Mike Pierce
    Jun 5 '15 at 4:26












  • $begingroup$
    @MikePierce Serious suggestion ?
    $endgroup$
    – callculus
    Jun 5 '15 at 4:33
















1












$begingroup$


Is it possible to have a set with the same mean, median, mode, and range?



If not, how can the following question be solved:




Set $H$ contains five positive integers such that the mean, median,
mode, and range are all equal. The sum of the data is $25$.



Using the above information, indicate which one will be greater:



a) the smallest possible number in set $H$.



b) 6.




If I assume that all the elements in set $H$ are equal to $5$, it doesn't satisfy the conditions for range, as the range will become zero then.






statistics means median







share|cite|improve this question











$endgroup$












  • $begingroup$
    The list ${0,0}$ works quite well for you first question.
    $endgroup$
    – Mike Pierce
    Jun 5 '15 at 4:26












  • $begingroup$
    @MikePierce Serious suggestion ?
    $endgroup$
    – callculus
    Jun 5 '15 at 4:33














1












1








1





$begingroup$


Is it possible to have a set with the same mean, median, mode, and range?



If not, how can the following question be solved:




Set $H$ contains five positive integers such that the mean, median,
mode, and range are all equal. The sum of the data is $25$.



Using the above information, indicate which one will be greater:



a) the smallest possible number in set $H$.



b) 6.




If I assume that all the elements in set $H$ are equal to $5$, it doesn't satisfy the conditions for range, as the range will become zero then.






statistics means median







share|cite|improve this question











$endgroup$




Is it possible to have a set with the same mean, median, mode, and range?



If not, how can the following question be solved:




Set $H$ contains five positive integers such that the mean, median,
mode, and range are all equal. The sum of the data is $25$.



Using the above information, indicate which one will be greater:



a) the smallest possible number in set $H$.



b) 6.




If I assume that all the elements in set $H$ are equal to $5$, it doesn't satisfy the conditions for range, as the range will become zero then.






statistics means median




statistics means median






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jun 5 '15 at 4:36









Ken

3,62151728




3,62151728










asked Jun 5 '15 at 4:17









India SlaverIndia Slaver

27118




27118












  • $begingroup$
    The list ${0,0}$ works quite well for you first question.
    $endgroup$
    – Mike Pierce
    Jun 5 '15 at 4:26












  • $begingroup$
    @MikePierce Serious suggestion ?
    $endgroup$
    – callculus
    Jun 5 '15 at 4:33


















  • $begingroup$
    The list ${0,0}$ works quite well for you first question.
    $endgroup$
    – Mike Pierce
    Jun 5 '15 at 4:26












  • $begingroup$
    @MikePierce Serious suggestion ?
    $endgroup$
    – callculus
    Jun 5 '15 at 4:33
















$begingroup$
The list ${0,0}$ works quite well for you first question.
$endgroup$
– Mike Pierce
Jun 5 '15 at 4:26






$begingroup$
The list ${0,0}$ works quite well for you first question.
$endgroup$
– Mike Pierce
Jun 5 '15 at 4:26














$begingroup$
@MikePierce Serious suggestion ?
$endgroup$
– callculus
Jun 5 '15 at 4:33




$begingroup$
@MikePierce Serious suggestion ?
$endgroup$
– callculus
Jun 5 '15 at 4:33










2 Answers
2






active

oldest

votes


















5












$begingroup$

The multiset $[3, 4, 5, 5, 8]$ will fit the bill.



You know, though, that even if you didn't have an example of a set on hand, the smallest element must be less than or equal to $5$ since the median is $5$ (since the mean is $5$).






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Of course, I knew that. This was so silly on my part that I didn't spend much time thinking about such a set. Thanks. :)
    $endgroup$
    – India Slaver
    Jun 5 '15 at 4:35





















3












$begingroup$

Hint: If I allow non-integers and let the set contain duplicates (I think duplicates are allowed, though generally a set does not allow them. To have a mode you need duplicates), ${2.5,5,5,5,7.5}$ satisfies the constraints. Can you modify it to use only integers?






share|cite|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









    5












    $begingroup$

    The multiset $[3, 4, 5, 5, 8]$ will fit the bill.



    You know, though, that even if you didn't have an example of a set on hand, the smallest element must be less than or equal to $5$ since the median is $5$ (since the mean is $5$).






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      Of course, I knew that. This was so silly on my part that I didn't spend much time thinking about such a set. Thanks. :)
      $endgroup$
      – India Slaver
      Jun 5 '15 at 4:35


















    5












    $begingroup$

    The multiset $[3, 4, 5, 5, 8]$ will fit the bill.



    You know, though, that even if you didn't have an example of a set on hand, the smallest element must be less than or equal to $5$ since the median is $5$ (since the mean is $5$).






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      Of course, I knew that. This was so silly on my part that I didn't spend much time thinking about such a set. Thanks. :)
      $endgroup$
      – India Slaver
      Jun 5 '15 at 4:35
















    5












    5








    5





    $begingroup$

    The multiset $[3, 4, 5, 5, 8]$ will fit the bill.



    You know, though, that even if you didn't have an example of a set on hand, the smallest element must be less than or equal to $5$ since the median is $5$ (since the mean is $5$).






    share|cite|improve this answer









    $endgroup$



    The multiset $[3, 4, 5, 5, 8]$ will fit the bill.



    You know, though, that even if you didn't have an example of a set on hand, the smallest element must be less than or equal to $5$ since the median is $5$ (since the mean is $5$).







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered Jun 5 '15 at 4:31









    KenKen

    3,62151728




    3,62151728












    • $begingroup$
      Of course, I knew that. This was so silly on my part that I didn't spend much time thinking about such a set. Thanks. :)
      $endgroup$
      – India Slaver
      Jun 5 '15 at 4:35




















    • $begingroup$
      Of course, I knew that. This was so silly on my part that I didn't spend much time thinking about such a set. Thanks. :)
      $endgroup$
      – India Slaver
      Jun 5 '15 at 4:35


















    $begingroup$
    Of course, I knew that. This was so silly on my part that I didn't spend much time thinking about such a set. Thanks. :)
    $endgroup$
    – India Slaver
    Jun 5 '15 at 4:35






    $begingroup$
    Of course, I knew that. This was so silly on my part that I didn't spend much time thinking about such a set. Thanks. :)
    $endgroup$
    – India Slaver
    Jun 5 '15 at 4:35













    3












    $begingroup$

    Hint: If I allow non-integers and let the set contain duplicates (I think duplicates are allowed, though generally a set does not allow them. To have a mode you need duplicates), ${2.5,5,5,5,7.5}$ satisfies the constraints. Can you modify it to use only integers?






    share|cite|improve this answer









    $endgroup$


















      3












      $begingroup$

      Hint: If I allow non-integers and let the set contain duplicates (I think duplicates are allowed, though generally a set does not allow them. To have a mode you need duplicates), ${2.5,5,5,5,7.5}$ satisfies the constraints. Can you modify it to use only integers?






      share|cite|improve this answer









      $endgroup$
















        3












        3








        3





        $begingroup$

        Hint: If I allow non-integers and let the set contain duplicates (I think duplicates are allowed, though generally a set does not allow them. To have a mode you need duplicates), ${2.5,5,5,5,7.5}$ satisfies the constraints. Can you modify it to use only integers?






        share|cite|improve this answer









        $endgroup$



        Hint: If I allow non-integers and let the set contain duplicates (I think duplicates are allowed, though generally a set does not allow them. To have a mode you need duplicates), ${2.5,5,5,5,7.5}$ satisfies the constraints. Can you modify it to use only integers?







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Jun 5 '15 at 4:27









        Ross MillikanRoss Millikan

        293k23197371




        293k23197371






























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