MathematicsA survey conducted on 20 households in a locality by a group of students resulted in the following frequency distribution table for the number of family members in a household.Find the mode of the data.

A survey conducted on 20 households in a locality by a group of students resulted in the following frequency distribution table for the number of family members in a household.


Find the mode of the data.


  1. A
    3.28
  2. B
    3.12
  3. C
    3.02
  4. D
    3.80 

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    Solution:

    The following frequency distribution table for the number of family members in a household is given.
    Mode is given as,
    Mode=l+f1 - f02f1- f0 - f2×h
    where 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.
    Here, the maximum frequency is 8 and the modal class=3-5.
    l=3, f0=7, f1=8, f2=2 and h=2.
    The mode of the data with maximum frequency 8 will be,
    Mode=3+8 - 72 (8) - 7- 2×2
    Mode=3+27
    Mode=3.28
    The mode of the data is 3.28.
    Hence, option 1 is correct.
     
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