If the mean of n observation 2x1, 2x2, 2xn is 2x - Maths - Statistics

Question

If the mean of n observation
2x 1 , 2x 2
, 2xn is 2x bar, show that

2x bar) = 0

Ajanta Trivedi · Accepted Answer

the mean of n observation 2x 1 , 2x 2 , 2xn is $2 \bar{x}$ i e $\frac{1}{n} \sum_{i = 1}^{n} 2 x_{i} = 2 \bar{x} \Rightarrow \sum_{i = 1}^{n} 2 x_{i} = 2 n \bar{x} \Rightarrow \sum_{i = 1}^{n} x_{i} = n \bar{x} (1)$ the LHS of the given is ; $\sum_{i = 1}^{n} (x_{i} - \bar{x}) = \sum_{i = 1}^{n} x_{i} - \sum_{i = 1}^{n} \bar{x} = \sum_{i = 1}^{n} x_{i} - \bar{x} \cdot \sum_{i = 1}^{n} 1 = n \bar{x} - n \bar{x} = 0$

If the mean of n observation 2x 1 , 2x 2 , .........2xn is 2x bar, show that 2x bar) = 0.

If the mean of n observation 2x ₁ , 2x ₂ , .........2x_n is 2x bar, show that

2x bar) = 0.