Mean, Median, and Range

Directions: Create a set of five positive integers from 1 to 20 that have the same mean, median, and range.

Hint

How do you find the mean/median/range of a set of five integers?

Answer

There are many answers including
{2, 3, 4, 5, 6} mean, median, range = 4
{3, 4, 6, 8, 9 } mean, median, range = 6
{3, 5, 6, 7, 9} mean, median, range = 6
{4, 6, 8, 10, 12} mean, median, range = 8
{4, 5, 8, 11, 12} mean, median, range = 8
{5, 8, 10, 12, 15} mean, median, range = 10
{6, 8, 12, 16, 20} mean, median, range = 12
{7, 8, 13, 17, 20} mean, median, range = 13
{6, 11, 14, 19, 20} mean, median, range = 14

Source: Eric Berchtold and Melissa Minnix

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30 comments

  1. I had a student come up with 2, 3, 4, 5, 6.

  2. Additional solutions:

    {4, 6, 8, 10, 12} mean, median, range = 8
    {7, 8, 13, 17, 20} mean, median, range = 13
    {6, 11, 14, 19, 20} mean, median, range = 14
    {4, 5, 8, 11, 12} mean, median, range = 8

  3. {3, 4, 6, 8, 9 } mean, median, range = 6
    {6, 8, 12, 16, 20} mean, median, range = 12
    {3, 5, 6, 7, 9} mean, median, range = 6

    • Thanks Eric and Dan for the extra solution sets.

    • Bibiana Rodriguez

      Additional solutions:

      {4, 5, 7, 8, 11} mean, median, range = 7
      {4, 7, 8, 9, 12} mean, median, range = 8
      {6, 12, 13, 15, 19} mean, median, range = 13
      {5, 9, 10, 11, 15} mean, median, range = 10

      One of the answers included is incorrect.
      {6, 8, 12, 16, 20} mean= 12.4 median= 12 range= 14

  4. The problem does not state that the whole numbers need to be unique whole numbers, so can a set include a mode? The set {3,3,5,6,8} contains 5 whole numbers whose mean, median, and range are 5.

    • Robert Kaplinsky

      I don’t see why not Tracey. That would be an interesting addition. I think the only reason it is not mentioned is because mode is not a Common Core State Standard.

  5. Nrich has a similar problem set which includes mode if some want to include it: https://nrich.maths.org/11281

  6. 2 plus 2 is 4 minus 1 is three quick maths

  7. My students found the following:
    6,7,10,11,16
    2,4,5,7,7
    5,15,15,20,20
    5,6,10,14,15
    4,9,10,13,14
    5,7,10,13,15
    4,8,9,11,13

  8. {2, 3, 4, 5, 6}=4 {3, 4, 6, 8, 9 } = 6 {3, 5, 6, 7, 9} = 6 {4, 6, 8, 10, 12} mean, median, range = 8
    {4, 5, 8, 11, 12} = 8 {5, 8, 10, 12, 15} = 10 {6, 8, 12, 16, 20}= 12 {7, 8, 13, 17, 20} = 13
    {6, 11, 14, 19, 20}= 14

  9. 2,3,6,9,3-mean4.6-median3-range7

  10. I got 2,2,2,4,4, mean, median, range=2

  11. whoops! I got mean & mode mixed up

  12. now I got 1,2,2,2,3, mean, median, range=2

  13. Wouldn’t 4, 4, 6, 6, 10 be an answer?
    Unless you can’t do modes.

  14. Wouldn’t 4, 4, 6, 6, 10 be an answer?
    Unless you can’t do modes

  15. Oops I sent it twice

  16. {2, 3, 4, 5, 6} mean, median, range = 4
    {6, 8, 12, 16, 20} mean, median, range = 12
    3, 5, 6, 7, 9} mean, median, range = 6

  17. There are many answers including
    {2, 3, 4, 5, 6} mean, median, range = 4
    {3, 4, 6, 8, 9 } mean, median, range = 6
    {3, 5, 6, 7, 9} mean, median, range = 6
    {4, 6, 8, 10, 12} mean, median, range = 8
    {4, 5, 8, 11, 12} mean, median, range = 8
    {5, 8, 10, 12, 15} mean, median, range = 10
    {6, 8, 12, 16, 20} mean, median, range = 12
    {7, 8, 13, 17, 20} mean, median, range = 13
    {6, 11, 14, 19, 20} mean, median, range = 14

  18. {6,11,14,19,20}mean,median,range=14
    {4,5,8,11,12} mean,median,range=8

  19. {2, 3, 4, 5, 6} mean, median, range = 4
    {3, 4, 6, 8, 9 } mean, median, range = 6
    {3, 5, 6, 7, 9} mean, median, range = 6
    {4, 6, 8, 10, 12} mean, median, range = 8
    {4, 5, 8, 11, 12} mean, median, range = 8
    {5, 8, 10, 12, 15} mean, median, range = 10
    {6, 8, 12, 16, 20} mean, median, range = 12
    {7, 8, 13, 17, 20} mean, median, range = 13
    {6, 11, 14, 19, 20} mean, median, range = 14

  20. Person aka kaleya

    {2, 3, 4, 5, 6} mean, median, range = 4
    {3, 4, 6, 8, 9 } mean, median, range = 6
    {3, 5, 6, 7, 9} mean, median, range = 6
    {4, 6, 8, 10, 12} mean, median, range = 8
    {4, 5, 8, 11, 12} mean, median, range = 8
    {5, 8, 10, 12, 15} mean, median, range = 10
    {6, 8, 12, 16, 20} mean, median, range = 12
    {7, 8, 13, 17, 20} mean, median, range = 13
    {6, 11, 14, 19, 20} mean, median, range = 14

  21. 6, 5, 6, 9, 7, 10, 6, 6, 8, 7
    I can’t find the mean , mode and median of this.

  22. {3, 6, 7, 9, 10} – mean, median and range =7

  23. Marjorie H Allred

    My students came up with 3,4,5,5,8 and not only are the mean, median and range equal to 5, but the mode is too.

  24. 2,3,4,5,6
    Mean: 2+3+4+5+6= 20
    20/5=4
    Median: 4
    Range: 6-2=4

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