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10th Class Mathematics Statistics Question Bank Statistics

  • question_answer
    The distribution below shows the number of wickets taken by bowlers in one - day cricket matches. Find the mean number of wickets by choosing a suitable method.
    Number of wickets Number of bowlers
    20 - 60 7
    60 - 100 5
    100 - 150 16
    150 - 250 12
    250 - 350 2
    350 - 450 3
     

    A)  133.67                        

    B)  145.23         

    C)  152.0             

    D)  152.89

    Correct Answer: D

    Solution :

    (d): Here, the class size varies, and the\[{{x}_{i}}s\] are large. Let us still apply the step deviation method with a = 200 and h = 20. Then, we obtain the data as in Table.
    Number of wickets taken Number of blowers \[({{f}_{i}})\] \[{{x}_{i}}\] \[{{d}_{i}}=\]\[{{x}_{i}}-200\] \[{{u}_{i}}=\frac{{{d}_{i}}}{20}\] \[{{u}_{i}}{{f}_{i}}\]
    20 ? 60 7 40 ? 160 ? 8 ? 56
    60 ? 100 5 8 ? 120 ? 6 ? 30
    100 ? 150 16 125 ? 75 ? 3.75 ? 60
    150 ? 250 12 200 0 0 0
    250 ? 350 2 300 100 5 10
    350 ? 450 3 400 200 10 30
    Total 45       ? 106
    \[\frac{\sum{{{f}_{i}}{{u}_{i}}}}{\sum{{{f}_{i}}}}=\frac{-106}{45}\]. Therefore, \[\overline{x}=200+20\left( \frac{-106}{45} \right)\] \[=200-47.11=152.89\] This tells us that, on an average, the number of wickets taken by theses 45 bowlers in one ? day cricket is 152.89.


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