MathematicsDetermine the missing frequency x, from the following data, when mode is 67 .

Determine the missing frequency x, from the following data, when mode is 67 .


  1. A
    10
  2. B
    8
  3. C
    5
  4. D
    12 

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    Solution:

    The following data is given and mode is given as 67.Mode is given as,
    Mode=l+f1 - f02f1- f0 - f2×h
    Here l is the lower limit of the modal class, h denotes the size of the class interval (assuming all class sizes to be equal), f1 is the frequency of the modal class, f0 is the frequency of the class preceding the modal class, and f2 is the frequency of the class succeeding the modal class.
    The mode for the given frequency distribution, the maximum frequency is 15 since mode is given as 67.
    So here, the modal class is 60-70, l=60, f1=15, f1=x and f2=12.
    Now to find the value of x, substitute the above values into the equation.
    Mode=l+f1 - f02f1- f0 - f2×h
    67=60+15 - x30 - x - 12×10
    0.7=15 - x18 - x
    0.3x=2.4
    x=8
    Hence, the value of x is 8.
    Therefore, option 2 is correct.
     
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