If the data x 1 , x 2 , … x 10 is 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

Question

If the data x 1 , x 2 , … x 10 is 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:

TestHub · Accepted Answer

Let the numbers are x 1 , x 2 , … x 10 N = 10 Given x 1 + x 2 + x 3 + x 4 = 4.11 = 44 x 5 + x 6 … . + x 10 = 6.16 = 96 ⇒ ∑ x i = 140 ⇒ variance σ 2 = ∑ x i 2 N - ∑ x i N 2 ⇒ σ 2 = 2000 10 - 140 10 2 ⇒ σ 2 = 200 - 196 = 4 ⇒ Standard deviation σ = 2 .

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