Five Digits

There are five single digit numbers hidden behind these clouds.

Cloud Cloud Cloud Cloud Cloud

Their mean, median, mode and range are all the same.
What are they?

This is a Transum Maths Lesson Starter Of The Day

Topics: Starter | Averages

  • Keeley Howe, Central Sussex college haywards heath England
  • 3 6 6 7 8

    mean = 6
    mode = 6
    median = 6
  • Mr Fogiel, Cults Academy
  • That answer is wrong - range is 5 not 6.

    0,0,0,0,0 works.
  • Certificate group, stoke college students
  • this problem doesnt show the range which is 5 not 6 as the other answers. our class has found that 2,4,4,4,6 gives the correct answers for ALL problems
  • Kangi Chalashika,
  • I have an answer to add 3,4,5,5,8

    range= 8 - 3 = 5

    Mode = 5

    Mean = (3+4+5+5+8)/5 = 5

    Median = 5
  • G & T Year 9, Vietnam
  • We generated the solutions
    1, 2, 2, 2, 3
    2, 4, 4, 4, 6
    3, 6, 6, 6, 9
    3, 4, 5, 5, 8
    0, 0, 0, 0, 0
    and discussed the concept of "families" of solutions and their general forms
    x, 2x, 2x, 2x, 3x and 3x, 4x, 5x, 5x, 8x respectively
    This allowed us to consider the idea of proof for these general solution forms
    great for the G & T group...
  • Mr Dunkley, A - Level
  • We loved this starter,
    we used a, b, c, d, e and came up with the formula
    2a + d = 2c
    b = c
    and e = a + c
    Then used these to generate the solutions:
    4, 11, 11, 14, 15
    5, 6, 8, 8, 13
    5, 11, 11, 12, 16
    5, 12, 12, 14, 17
    5, 13, 13, 16, 18
    5, 14, 14, 18, 19
    7, 15, 15, 16, 22
    These in turn are generaters of there own families!
    Excellent starter.
  • 8b1 G And T, Seaham School
  • 1,2,2,2,3 then double them 2,4,4,4,6
    3,4,5,5,8 and 3,6,6,6,9.
    We thought about 0,0,0,0,0 but it has no mode.
  • Celeste V., Santa Clara Primary School - Western Australia
  • Another solution
    2 6 6 8 8
    Mean = 6
    Median = 6
    Mode = 6
    Range = 6.
  • Mr T, Sydney, Australia
  • Some comments here appear to have forgotten that the initial question actually asked for single digit answers, as pointed out by a student in my excellent Year 11 Class.
  • Hanxiao, China
  • 0,0,0,0,0
  • Cameron Evans- Thompson Y6, Goldington Middle, Bedford
  • 2, 5, 5, 6, 7
    median = 5
    mode = 5
    range = 5
    mean = 5.
  • Caldecott Foundation School, Class 6 - Y10
  • 1,2,2,2,3
    6,12,12,12,18 :P
    We found out that the numbers go up in tables.
    The first number uses the one times table, the second, third and fourth, the two times table and the fifth number the three times table.
    We can use the expression
    n, 2n, 2n, 2n, 3n to describe this.
  • Thomas's Clapham, Year 6 13+ A Set
  • An excellent way to consolidate these skills
    Year 6(13+) A set collectively found all 5 possible combinations!
  • Derek, Torry Academy
  • 1 3 3 4 4 works if you allow both 3 and 4 to be the mode.
  • Roy Froud, Bournemouth
  • [182736]
    not given so far is 2 2 3 3 5
    (if 2 modes are allowed)
    Algebraic conditions are either that:
    a + 2(m - a) + m + m +(a + m) = 5m,
    a + m + m + 2(m - a) +(a + m) = 5m,
    Where m is the mean, mode, median and range and "a" is the first term.
    In the first equation m is greater than 2(m - a) and in the second eqution m is less than 2(m - a).
  • Roy Froud, Bournemouth
  • I left out some words in my comment on 10 february. There should be the word "or" between the two equations and the words "or equal to" after "less than" and "greater than".
    Only 8 solutions for single digit numbers 1 to 9 (no nonsense zeros) for when m is less than 2a (2 answers), m = 2a (3 answers) and m greater than 2a (3 answers).
    All have been given.
  • Year 8 Set 1, Spalding High School, Lincolnshire
  • We found the following solutions;
    2,5,5,6,7 and 2,4,4,4,6
    Really enjoyed this starter as it got us thinking about averages and how changing just one value in the list affects the averages overall. It also promoted a good discussion about the value 0.
    Thank you very much!
  • Mrs. Soupa, Barnes
  • We got 3, 2, 2, 2, 1
    We really enjoyed the starter, and were keen to get onto the main course!
  • Fulham Prep School, 7R
  • The class enjoyed this activity. It was good to check each others answers.
    We found:
  • Marianne, BSK British School Of Kuwait Yr10 Set 1
  • Marianne so rightly pointed out that the question specified SINGLE DIGIT numbers. An A-Level class have used double digit numbers ;-).
  • Mr Wilson, Denver, Colorado
  • Jack in our class, got the numbers 3,6,6,6,9. He is only in Year 3 as well!
  • Mr Parsons, Ashcroft High School
  • I love these questions. It makes you think. I will use this as a lesson started with my smart year 8 students tomorrow.
  • Glen, Brentwood
  • I would argue that a multiple mode solution, e.g. {2,2,3,3,5}, is a contradiction. I.e. the mode equals the mean, and the mode does not equal the mean. I would also argue for allowing {0,0,0,0,0} as a solution.
    Our results are: {0,0,0,0,0}, {1,2,2,2,3}, {2,4,4,4,6}, {3,6,6,6,9}, {2,5,5,6,7}, {3,4,5,5,8}.
    Nice problem, thanks.
  • Maths Department TEA, Kuwait
  • a,b,c,d,e
    for example(1,2,2,2,3) or (2,4,4,4,6).

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.

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Laptops In Lessons

Teacher, do your students have access to computers such as tablets, iPads or Laptops?  This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments:

However it would be better to assign one of the student interactive activities below.

Laptops In Lessons

Here is the URL which will take them to an exercise on averages.

Student Activity


Curriculum Reference

See the National Curriculum page for links to related online activities and resources.


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