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10th Class Mathematics Statistics Question Bank Statistics

  • question_answer
    Let \[{{x}_{1}},{{x}_{2}},.....,{{x}_{n}}\] be n observations. Let \[{{w}_{i}}=1{{x}_{i}}+k\] for = 1, 2, 3, ........ n where 1 and k are constants. If the mean of \[{{x}_{i}}s\]. is 48 and their S.D. is 12; the mean of \[{{w}_{i}}'s\] is 55 and their S. D. is 15, then the value of 1 and k are respectively

    A)  1.25, 5            

    B)  2, 5           

    C)  2 - 5                           

    D)  1.25, - 5

    Correct Answer: D

    Solution :

    (d): \[\overline{w}=1\overline{x}+k\] and \[{{\sigma }_{w}}\ne 1{{\sigma }_{x}}\] \[\Rightarrow 55=48\,1+k\]__________(1) And \[15=12|1|\]­­­­­­­­__________(2) From (2), |1| \[=\frac{15}{12}=\frac{5}{4}\Rightarrow 1=1.25\] or \[-1.25\]. If 1 = 1.25, then from (1), \[k=55-48\times 1.25\]                                     \[=-5\] And if 1 = ? 1.25, then from (1), \[k=55-48\times (-1.25)=55+60=115\] Thus, 1 = 1.25 and k = ? 5 and this corresponds to the values given in (d)


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