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Statement-1 :The A.M. of series 1,2,4,8,...

Statement-1 :The A.M. of series 1,2,4,8,16,…… `2^n` is `(2^(n+1)-1)/(n+1)`
Statement-2 : Arithmetic mean (A.M.) of ungrouped data is `(Sigmax_i)/n` where `x_1,x_2`…. `x_n` are n numbers .

A

Statement-1 is True, Statement-2 is True , Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True , Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True , Statement-2 is False

D

Statement-1 is False , Statement-2 is True

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The A.M.of the series 1,2,4,8,16,...,2^(n) is

Statement-1 : The mean of the series x_1, x_2 ,….. x_n is x. If x_2 is replaced by lambda then new mean is independent of lambda Statement-2 : barx (mean)= (x_1+x_2+…. +x_n)/n

Knowledge Check

  • The Am of the series 1,2,4,8,16,…,2^n is

    A
    `(2^n-1)/n`
    B
    `(2^(n+1)-1)/n`
    C
    `(2^n+1)/n`
    D
    `(2^n-1)/(n+1)`

  • The arithmetic mean of the series 1,2,2^(2) ,…….2^(n-1) is

    A
    `2^(n)//n`
    B
    ` (2^(n) -1) //n`
    C
    ` (2^(n+1) )//n`
    D
    none of these

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    Statement-1 : The mean deviation of the numbers 3,4,5,6,7 is 1.2 Statement-2 :mean deviation = (Sigma_(i=1)^(n) |x_i-barx|)/n .

    The arithmetic mean of the series 1,2,4,8,16,....2^(n) is (2^(n)-1)/(n+1) (b) (2^(n)+1)/(n) (c) (2^(n)-1)/(n) (d) (2^(n+1)-1)/(n+1)

    Statement 1: The variance of first n even natural numbers is (n^2-1)/4 Statement 2: The sum of first n natural numbers is (n(n+1)/2 and the sum of squares of first n natural numbers is (n(n+1)(2n+1)/6 (1) Statement1 is true, Statement2 is true, Statement2 is a correct explanation for statement1 (2) Statement1 is true, Statement2 is true; Statement2 is not a correct explanation for statement1. (3) Statement1 is true, statement2 is false. (4) Statement1 is false, Statement2 is true

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