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JEE Main & Advanced JEE Main Paper (Held on 7 May 2012)

  • question_answer
    The frequency distribution of daily working expenditure of families in a locality is as follows:
    Expenditure in Rs. (x): 0-50 50-100 100-150 150-200 200-250
    No. of families (f): 24 33 37 B 25
    If the mode of the distribution is " 140, then the value of b is   JEE Main Online Paper (Held On 07 May 2012)

    A) 34                                          

    B) 31

    C) 26                                          

    D) 36

    Correct Answer: D

    Solution :

    Frequency distribution is given as
    Expenditure No. of families (f)
    0-50 24
    50-100 33
    100-150 37
    150-200 B
    200-250 25
    Clearly, modal class is 100-150, as the maximum frequency occurs in this class. Given, Mode = 140     We have Mode\[=\ell +\frac{{{f}_{0}}-{{f}_{-1}}}{2{{f}_{0}}-{{f}_{-1}}-{{f}_{1}}}\times i\]where \[\ell =100,{{f}_{0}}=37,{{f}_{-1}}=33,{{f}_{1}}=b\]\[i=50\] Thus, we get \[140=100+\left[ \frac{37-33}{2\left( 37 \right)-33-b} \right]\times 50\] \[=100+\frac{200}{41-b}\] \[\Rightarrow \]5740=4300+40b\[\Rightarrow \]b=36


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