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

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

  1. mmmmmaths

    mmmmmaths New commenter

    sorry to confuse....post 16 I meant my answer was to Mathsmanuk.


    mathsgenius, why not cumulative frequency polygons?

    At GCSE they need to be able to draw cumulative frequency diagram(s) . If the data is continuous they can join the points with either lines or a curve to get the marks, but if asked for a polygon they will need to use straight lines.
     
  2. Mathsteach2

    Mathsteach2 Established commenter

    I am not a qualified maths teacher (mine is physics) and I am certainly not a statistician. However, I do some private tuition here in Barbados, and one of my students (CXC - Caribbean equiv GCSE) told me his teacher says to plot a cumulative frequency curve using grouped data, the cf (on the y-axis) is plotted against the upper class limit of the class. However, his textbook (Oxford Mathematics for the Caribbean Book 4)says cf should be plotted against the upper class boundary. In one example from the text I plotted both on the same graph, and as a physics teacher identified serious errors in reading off the ogives drawn, amounting to + or - two whole persons on the cf axis. (The data were the times for 100 walkers in a race, grouped to within + or - 2 mins) The answer in the text clearly gave an exact number of walkers (how many won a prize, coming in less than 65 mins), I had to draw the graph on cmxcm paper, fine lines 2mm, and needed that degree of accuracy just to plot the points to + or - 1mm. To get decent smooth curves I had to shade in a band (not a line) nearly 3mm wide to accommodate all of the data. Was my physics getting in the
    way of the maths!?
    A maths website says the points on an ogive should be joined with straight lines. This makes sense to me, as the cf is clearly not continuous data in this example (and was news to me, since no school textbook I have seen has said that - but to join the points with a smooth curve). Interesting, doing this very carefully on my graph (to an accuracy of + or - 0.5 mm on the graph paper) clearly shows the textbook answer to be incorrect by one whole person.
    (Someone didn't get a prize which could be trouble for the maths teacher helping on school sports day!).

     
  3. Mathsteach2

    Mathsteach2 Established commenter

    I have resuurected this thread having found the following:

    "The points should be connected by straight lines, not a smooth curve as taught by many textbooks. The straight line assumes that the data are uniformly distributed across the class interval - as represented on a histogram by a rectangular bar. Whilst this will almost certainly not be true, it gives an objective view that allows different people to come to common conclusions. Connecting the points by a smooth curve is subjective and will lead to different people drawing different conclusions from the data."

    Taken from:

    http:/home.ched.coventry.ac.uk/Volume/vol0/ogive.htm
     
  4. flymaths

    flymaths New commenter

    Thanks for that Mathsteach2 - I guess it's important to keep an eye on the opinions of the exam boards on this overall!
     
  5. blue117

    blue117 New commenter

    About 3 years ago our dept received 'advice' that cumulative frequency graphs could be either. This advice must have come from the board (OCR) because I can remember discussing it with my GCSE students who were doing coursework (and stats coursework is enough of a minefield, without giving kids bad advice)
     

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