If the data is x1,x2, …x10 such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of all of these is 2000; then the standard deviation of this data is

If the data is x1,x2, x10 such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of all of these is 2000; then the standard deviation of this data is

  1. A

    2

  2. B

    22

  3. C

    4

  4. D

    2

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    Solution:

    Given, x1+x2+x3+x44=11

    x1+x2+x3+x4=44(i)

    Also, x5+x6+x7+x8+x9+x106=96(ii)

    from (i) and (ii),i=110xi=44+96=140

    Now, Variance σ2=i=110xi210i=110xi102

    =200010140102  Given i=110xi2=2000=200196=4

     Standard deviation (σ)=2

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