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10th Class Mathematics Statistics Question Bank Statistics

  • question_answer
    In an examination of 675 candidates of maximum marks 100 the examiner supplied the following information.
    Marks obtained No. of candidates
    Less than 10%       7
    Less than 20% 39
    Less than 30% 95
    Less than 40% 201
    Less than 50% 381
    Less than 60% 545
    Less than 70% 631
    Less than 80%      675
    Calculate median and mode respectively of the percentage marks optained.

    A)  47.58, 46.33 

    B)  49.12, 48.22  

    C)  45.24, 46.22              

    D)  47.58, 48.22

    Correct Answer: D

    Solution :

    Marks  \[({{f}_{i}})\] cf Frequency
    0-10 7 7
    10-20 39 32
    20-30 95 56
    30-40 201 106
    40-50 381 180
    50-60 545 164
    60-70 631 86
    70-80 675 44
    Here, \[n=675\,\,\,\,\Rightarrow \,\,\,\frac{n}{2}=337.5\] So, Median class \[40-50\]. Median \[=l+\left( \frac{\frac{n}{2}-cf}{f} \right)\times h\] \[=40+7.58=47.58\] Now, maximum frequency is 180.             So, modal class is\[40-50\].                   Modes  \[=l+\left( \frac{{{f}_{1}}-{{f}_{0}}}{2{{f}_{1}}-{{f}_{0}}-{{f}_{2}}} \right)\times h\] \[=40+\left( \frac{180-106}{2\times 180-106-164} \right)\times 10\] \[=40+\frac{74}{90}\times 10=40+8.22=48.22\]


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