Keywords: Starter | Averages

• Keeley Howe, Central Sussex college haywards heath England
• Thursday, November 08, 2007
• "3 6 6 7 8
  
  mean = 6
  mode = 6
  median = 6"
• Mr Fogiel, Cults Academy
• Friday, November 09, 2007
• "That answer is wrong - range is 5 not 6.
  
  0,0,0,0,0 works."
• Certificate group, stoke college students
• Friday, November 09, 2007
• "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,
• Saturday, May 17, 2008
• "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
• Tuesday, November 11, 2008
• "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
• Wednesday, March 04, 2009
• "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
• Monday, January 18, 2010
• "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
• Tuesday, November 09, 2010
• "Another solution
  2 6 6 8 8
  Mean = 6
  Median = 6
  Mode = 6
  Range = 6."
• Mr T, Sydney, Australia
• Tuesday, November 09, 2010
• "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
• Tuesday, November 09, 2010
• "0,0,0,0,0
  1,2,2,2,3
  2,4,4,4,6
  3,6,6,6,9."
• Cameron Evans- Thompson Y6, Goldington Middle, Bedford
• Tuesday, November 09, 2010
• "2, 5, 5, 6, 7
  median = 5
  mode = 5
  range = 5
  mean = 5."
• Caldecott Foundation School, Class 6 - Y10
• Tuesday, November 09, 2010
• "1,2,2,2,3
  2,4,4,4,6
  3,6,6,6,9
  4,8,8,8,12
  5,10,10,10,15
  6,12,12,12,18 :P
  7,14,14,14,21
  8,16,16,16,24
  9,18,18,18,27
  10,20,20,20,30
  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
• Wednesday, November 10, 2010
• "An excellent way to consolidate these skills
  Year 6(13+) A set collectively found all 5 possible combinations!
  1,2,2,2,3
  2,4,4,4,6
  3,4,5,5,8
  2,5,5,6,7
  3,6,6,6,9."
• Derek, Torry Academy
• Thursday, November 11, 2010
• "1 3 3 4 4 works if you allow both 3 and 4 to be the mode."
• Roy Froud, Bournemouth
• Thursday, February 10, 2011
• "[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
• Sunday, February 13, 2011
• "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
• Thursday, March 31, 2011
• "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
• Wednesday, November 09, 2011
• "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
• Tuesday, November 22, 2011
• "The class enjoyed this activity. It was good to check each others answers.
  We found:
  3,5,5,4,8."

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This starter has scored a mean of 3.7 out of 5 based on 88 votes.

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