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10th Class Mathematics Statistics Question Bank Statistics

  • question_answer
    Find the median for the following distribution of workers.
    Daily wages No. of workers Daily wages No. of workers
    1-3 6 9-11 21
    3-5 53 11-13 16
    5-7 85 13-15 4
    7-9 86 15-17 4

    A)  \[7.14\]                       

    B)  \[6.84\]                       

    C)  \[5.92\]                       

    D)  \[5.57\]

    Correct Answer: B

    Solution :

    Daily wages No of workers Cumulative Frequency (cf)
    1-3 6 6
    3-5 53 59
    5-7 85 144
    7-9 86 230
    9-11 21 251
    11-13 16 267
    13-15 4 271
    15-17 4 275
    Here, \[n=275\,\,\,\Rightarrow \,\,\,\frac{n}{2}=137.5\] Median class is \[5-7\] Median \[=l+\left( \frac{\frac{n}{2}-cf}{f} \right)\times h\] \[=5+\left( \frac{137.5-59}{85} \right)\times 2=5+\frac{78.5}{85}\times 2\] \[=5+1.84=6.84\]


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