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Math Help - mean, median, mode and range

  1. #1
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    mean, median, mode and range

    hi, i need to know what the mean, median, mode and range would be for this table. could you explain how you got your answers so i understand! mean, median, mode and range-untitled.jpg
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  2. #2
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    Mode

    The x value of 10 has the highest frequency (11). Therefore, the mode is 10.

    Mean


    To find the mean, a new set of values must be added to the frequency table. This set of values will be called "x * Frequency". In this set of values, the values equal to x multiplied by the frequency. So the values are: 30, 42, 16, 63, 110.

    The mean can then be calculated using the formula:
    Mean = \frac{Sum of (x * Frequency)}{Total Frequency}
    Mean = \frac{261}{31}
    Mean = 8.4 (Rounded 1 decimal place)

    Therefore the mean is 8.4.

    Median

    To find the mean, first add up all the frequency values.
    5 + 6 + 2 + 7 + 11 = 31

    Because the number (31) is odd, the median is at the 16th position.
    (\frac{n + 1}{2}) = (\frac{31 + 1}{2}) = 16

    To find out the 16th position, add up the frequencies as follows:

    x: 6, 7, 8, 9, 10
    F: 5, 6, 2, 7, 11
    P: 5, (5 + 6)= 11, (11 + 2) = 13, (13 + 7) = 20, (20 + 11) = 31

    The 16th position is after the 13th position and before the 20th position.

    Therefore the median is 9.
    Last edited by RogueDemon; March 19th 2010 at 10:27 AM. Reason: Median is 9***
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  3. #3
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    Quote Originally Posted by RogueDemon View Post
    Mode

    The x value of 10 has the highest frequency (11). Therefore, the mode is 10.

    Mean


    To find the mean, a new set of values must be added to the frequency table. This set of values will be called "x * Frequency". In this set of values, the values equal to x multiplied by the frequency. So the values are: 30, 42, 16, 63, 110.

    The mean can then be calculated using the formula:
    Mean = \frac{Sum of (x * Frequency)}{Total Frequency}
    Mean = \frac{261}{31}
    Mean = 8.4 (Rounded 1 decimal place)

    Therefore the mean is 8.4.

    Median

    To find the mean, first add up all the frequency values.
    5 + 6 + 2 + 7 + 11 = 31

    Because the number (31) is odd, the median is at the 16th position.
    (\frac{n + 1}{2}) = (\frac{31 + 1}{2}) = 16

    To find out the 16th position, add up the frequencies as follows:

    x: 6, 7, 8, 9, 10
    F: 5, 6, 2, 7, 11
    P: 5, (5 + 6)= 11, (11 + 2) = 13, (13 + 7) = 20, (20 + 11) = 31

    The 16th position is after the 13th position and the 20th position.

    Therefore the median is 7.
    thanks very much, do you know how to do the range?
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  4. #4
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    Range

    The range of x can be calculated as follows:

    r = (greatest value in set) - (lowest value in set)
    r = 10 - 6
    r = 4

    Therefore the range of x is 4.
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  5. #5
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    Range is MAX - MIN, like already stated.
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