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Cumulative Frequency diagram - drawing curve with straight lines???

Discussion in 'Mathematics' started by flymaths, Sep 25, 2006.

  1. flymaths

    flymaths New commenter

    Dear all,

    We've just started using a new series of textbooks and in the section on cumulative frequency diagrams the points are joined up with a ruler and straight lines and not a smooth curve.

    Am I right in thinking that this isn't right and they should be joined up smoothly by hand?

    Any opinions would be gratefully received.
     
  2. flymaths

    flymaths New commenter

    Dear all,

    We've just started using a new series of textbooks and in the section on cumulative frequency diagrams the points are joined up with a ruler and straight lines and not a smooth curve.

    Am I right in thinking that this isn't right and they should be joined up smoothly by hand?

    Any opinions would be gratefully received.
     
  3. bbibbler

    bbibbler New commenter

    Smooth line definantly

    Straight would overestimate intoperlation below the median and underestimate above
     
  4. Smooth Curve for me
     
  5. I'll third that - I've never seen a cumulative frequency curve drawn with line segments.
     
  6. Colleen_Young

    Colleen_Young Occasional commenter

    I havn't seen a cf curve with straight lines but have seen plenty of 'cumulative frequency polygons' with straight line segments.

    see extract from mathsnet:

    Cumulative Frequency
    This is the running total of the frequencies. On a graph, it can be represented by a cumulative frequency polygon, where straight lines join up the points, or a cumulative frequency curve.

     
  7. The diagram can be represented by a cumulative frequency polygon, where straight lines join up the points, or a cumulative frequency curve. Both are viable as far as I am aware.
     
  8. bbibbler

    bbibbler New commenter

    What use is the polygon?
     
  9. flymaths

    flymaths New commenter

    Thanks for the prompt replies, everyone - will make sure I use other examples rather than the ones in the text when I go through this!
     
  10. Polygon: assumes data is evenly spread through the given interval

    Curve: assumes data is "bell shaped" ie more in the middle [for an S-shape anyway... not sure otherwise]

    In exams a polygon will always get you the marks (if asked to do a curve you will get marks both ways I think)

    Also a polygon is easier to draw through the points!
     
  11. This is why I dislike statistics! It is not real maths and should not be included with real maths for GCSE but kept as a separate exam. I had never heard of a cumulative frequency curve (or polygon) until after I got my degree.
     
  12. bbibbler

    bbibbler New commenter

    Not when I have marked Exams

    3 years ago in AQA stats, the marking instruction specically excluded straight lines
     
  13. flymaths

    flymaths New commenter

    That's interesting - it's in the textbook that's been written for the AQA course!
     
  14. At coursework moderation meeting 2 or 3 years ago we were told that ***. freq. polygons were essential for coursework (unless discrete data when c.f.step polygons must be used) due to size of sample - too small to draw c.f. curve.

    Are we the only school told this?
     
  15. Should have said AQA exam board - Stats and Maths moderator
     
  16. Out of interest...

    Why/when use a frequency step polygon?
     
  17. mmmmmaths

    mmmmmaths New commenter

    post 16

    for discete data
     
  18. Not just post-16, all GCSE coursework moderated down because they had not used cf step polygons for Read All About It (and word length is discrete).

    Is this just our moderator - does no-one else have to do this?
     
  19. I believe that you should only use cummulative frequency curves with continuous data and step ploygons with discrete data. The fact that your cummulative frequency curve has straight line defeats the purpose of representing continuous data.

    Hope this helps
     

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