Question

The mean of the values 1, 2, 3, …….n with respective frequencies x, 2x, 3x …… nx is:

Answer 1

Answer:

The mean of the values 1, 2, 3, …….n with respective frequencies x, 2x, 3x …… nx is:

⅓(2n+1).  

Step-by-step explanation:

[ (1)(x) + (2)(2x) + (3)(3x) + ... + (n)(nx) ] / (x+2x+3x+...+nx)  

= x(1² + 2² + 3² + ... + n²) / x(1+2+3+...+n)  

= (1² + 2² + 3² + ... + n²) / (1+2+3+...+n)  

= n(n+1)(2n+1)/6 ÷ n(n+1)/2  

= ⅓(2n+1).  

Answer 2

Answer:

Step-by-step explanation:

The mean of frequency

Mean = ∑ fi xi/ Number of observation

∑fixi = x + 2²x +3²x +......n²x

       = x ( 1 + 2²+3²+...n²)

       = x n ( n +1) ( 2n+1) /6

{ ∵ 1 + 2²+3²+..n² = n (n+1) (2n +1 )/6}

Number of observation = n

Mean = x n ( n+1) (2n +1) / n×6

          = x (n+1) (2n +1) /6