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JEE Main & Advanced Sample Paper JEE Main Sample Paper-39

  • question_answer
    The S.D. of the following data is nearly
    \[{{x}_{i}}\] 140 145 150 155 160 165 170 175
    \[{{f}_{i}}\] 4 6 15 30 36 24 8 2

    A)  8.64                           

    B)  7.26

    C)  7.05                           

    D)  None

    Correct Answer: B

    Solution :

     Let us assume an arbitrary mean a = 155. Following table is constructed :
    \[{{\text{X}}_{\text{i}}}\] \[{{\text{f}}_{\text{i}}}\] \[{{u}_{\text{i}}}=\frac{{{X}_{i}}-155}{5}\] \[u_{i}^{2}\] \[{{f}_{i}}{{u}_{i}}\] \[{{f}_{i}}u_{i}^{2}\]
    140 4 -3 9 -12 36
    145 6 -2 4 -12 24
    150 15 -1 1 -15 15
    155 30 0 0 0 0
    160 36 1 1 36 36
    165 24 2 4 48 96
    170 8 3 9 24 72
    175 2 4 16 8 32
    Total 125 77 311
    \[\therefore \]Variance, \[{{\sigma }^{2}}={{c}^{2}}\left( \frac{\sum\limits_{{}}^{{}}{{{f}_{i}}u_{1}^{2}}}{n}-{{\left( \frac{\sum\limits_{{}}^{{}}{{{f}_{i}}u_{1}^{2}}}{n} \right)}^{2}} \right)\]


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