1. If the mean of the numbers \(x_1, x_2, x_3, x_4, ..., x_n\) is \(\bar{x}\), then the value of \((x_1 - \bar{x}) + (x_2 - \bar{x}) + (x_3 - \bar{x}) + ... + (x_n - \bar{x})\) will be —

(a) 0 (b) 1 (c) 3 (d) 5

2. If the average of the quantities \(x_1, x_2, x_3,.......,x_{10}\) is 20, then the average of \(x_1+4, x_2+4, x_3+4,...., x_{10}+4\) will be—?

(a) 20 (b) 24 (c) 40 (d) 10

3. If the mean of \(x_1, x_2, x_3, ....., x_n\) is \(\bar{x}\), then the mean of \(x_1 + k, x_2 + k, x_3 + k, ....., x_n + k\) will be _____.

4. If the average of \(x_1, x_2, x_3, \ldots, x_n\) is \(\bar{x}\), then the average of \(ax_1, ax_2, ax_3, \ldots, ax_n\) is ________, where \(a ≠ 0\).

5. If the average of \(x_1, x_2, x_3, ... , x_n\) is \(\bar{x}\), then the average of \(k + x_1, k + x_2, k + x_3, ... , k + x_n\) is \(k + \bar{x}\).