2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Statistics

JEE Main & Advanced Mathematics Statistics Question Bank Measures of dispersion

  • question_answer
    What is the standard deviation of the following series [DCE 1996]
    Measurements 0-10 10-20 20-30 30-40
    Frequency 1 3 4 2

    A)                 81           

    B)                 7.6

    C)                 9             

    D)                 2.26

    Correct Answer: C

    Solution :

                      
    Class fi yi \[d={{y}_{i}}-A\], A = 25 fidi fidi2
    0-10 1 5 ? 20 ? 20 400
    10-20 3 15 ? 10 ? 30 300
    20-30 4 25 0 0 0
    30-40 2 35 10 20 200
    Total 10 ? 30 900
          \[{{\sigma }^{2}}=\frac{\sum {{f}_{i}}d_{i}^{2}}{\sum {{f}_{i}}}-{{\left( \frac{\sum {{f}_{i}}{{d}_{i}}}{\sum {{f}_{i}}} \right)}^{2}}=\frac{900}{10}-{{\left( \frac{-30}{10} \right)}^{2}}\]                    \[{{\sigma }^{2}}=90-9=81\]Þ s = 9.


You need to login to perform this action.
You will be redirected in 3 sec spinner