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Math Help - mean of grouped frequeny table

  1. #1
    Senior Member furor celtica's Avatar
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    mean of grouped frequeny table

    The standardised marks received by 318 students who took a mechanics examinations are summarised in the following grouped frequency table.

    Mark 0-29 30-39 40-49 50-59 60-69 70-79 80-89 90-100
    Frequency 12 7 13 25 46 78 105 32

    Iím supposed to find the mean of these data, which should be fairly straightforward: sigma(xf)/sigma(f) taking mid-class values for x: 15, 35, 45, 55, 65, 75, 85, 95
    So the mean = (15x12 + 35x7 + 45x13 + 55x25 + 65x46 + 75x78 + 85x105 + 95x32)/(318) = 72.9 to 3 s.f.
    But the answer is 72.5, and I really donít understand how to get there. Does this have something to do with conventional class boundaries, such as -0.5 to 29.5 for marks 0-29, 89.5 to 100.5 for marks 90-100, etc.? But I thought these were just for convention, I donít see how they could alter the mean. Any hints would be appreciated
    Sorry if this is unnecessarily detailed btw
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by furor celtica View Post
    The standardised marks received by 318 students who took a mechanics examinations are summarised in the following grouped frequency table.

    Mark 0-29 30-39 40-49 50-59 60-69 70-79 80-89 90-100
    Frequency 12 7 13 25 46 78 105 32

    I’m supposed to find the mean of these data, which should be fairly straightforward: sigma(xf)/sigma(f) taking mid-class values for x: 15, 35, 45, 55, 65, 75, 85, 95
    So the mean = (15x12 + 35x7 + 45x13 + 55x25 + 65x46 + 75x78 + 85x105 + 95x32)/(318) = 72.9 to 3 s.f.
    But the answer is 72.5, and I really don’t understand how to get there. Does this have something to do with conventional class boundaries, such as -0.5 to 29.5 for marks 0-29, 89.5 to 100.5 for marks 90-100, etc.? But I thought these were just for convention, I don’t see how they could alter the mean. Any hints would be appreciated
    Sorry if this is unnecessarily detailed btw
    Check what you are using for mid class marks. The first class contains marks from 0 to 29, with a mid class mark of 14.5, the second ...

    (the marks are all integers)

    CB
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