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10th Class Mathematics Statistics Question Bank Statistics

  • question_answer
    The median of the following data is 525. Find the missing frequencies, if it is given that there are 100 observations in the data.
    Class Interval Frequency Class  Frequency
    0-100 2 500-600 20
    100-200 5 600-700 \[{{f}_{2}}\]
    200-300 \[{{f}_{1}}\] 700-800 9
    300-400 12 800-900 7
    400-500 17 900-1000 4

    A)  8, 14                          

    B)  11, 17        

    C)                     9, 15                          

    D)  10, 16        

    Correct Answer: C

    Solution :

    Class interval \[({{x}_{i}})\] Frequency \[({{f}_{i}})\] Cumulative frequency
    0-100 50 2 2
    100-200 150 5 7
    200-300 250 \[{{f}_{1}}\] \[7+{{f}_{1}}\]
    300-400 350 12 \[19+{{f}_{1}}\]
    400-500 450 17 \[36+{{f}_{1}}\]
    500-600 550 20 \[56+{{f}_{1}}\]
    600-700 650 \[{{f}_{2}}\] \[56+{{f}_{1}}+{{f}_{2}}\]
    700-800 750 9 \[65+{{f}_{1}}+{{f}_{2}}\]
    800-900 850 7 \[72+{{f}_{1}}+{{f}_{2}}\]
    900-1000 950 4 \[76+{{f}_{1}}+{{f}_{2}}\]
    We have given             \[n=100\,\,\,\Rightarrow \,\,76+{{f}_{1}}+{{f}_{2}}=100\] \[\Rightarrow \]  \[{{f}_{1}}+{{f}_{2}}=24\]                     ?..(i) Since median is 525, so median class is\[500-600\]. Median \[=l+\left( \frac{\frac{n}{2}-cf}{f} \right)\times h\] \[\Rightarrow \]\[525=500+\frac{50-(36+{{f}_{1}})}{20}\times 100\]      \[\Rightarrow \]  \[25=(14-{{f}_{1}})\times 5\,\,\,\Rightarrow \,\,25=70-5{{f}_{1}}\] \[\Rightarrow \]   \[5{{f}_{1}}=45\,\,\,\,\Rightarrow \,\,\,\,{{f}_{1}}=9\] From (i), \[9+{{f}_{2}}=24\,\,\,\Rightarrow \,\,\,{{f}_{2}}=24-9=15\]


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