1. Let x be the mean of x₁, x₂, ...x_nand y be the mean of y₁, y₂....y_n. If z is the mean of of x₁, x₂, ...x_n'y₁, y₂....y_n. then z is equal to?

2. If each observation is increased by 5, then their mean

(a) remains the same (b)becomes 5 times the original mean (c) is decreased by 5 (d) is increased by 5.

Please answer with explanation.

Let x be the mean of x₁, x₂, ...x_nand y be the mean of y₁, y₂....y_n. If z is the mean of of x₁, x₂, ...x_{n '}y₁, y₂....y_n. then z is equal to?

1)

Given, x  be the mean of x₁, x₂, ...x_nand y be the mean of y₁, y₂....y_n. Also, z is the collective mean of x₁, x₂, ...x_{n '}y₁, y₂....y_n.

Also,

Now, 

2)

Let there are n observations as follows:

a ₁, a ₂, a ₃ ...., a_n

The mean of above observations is given by:

Now each observation is increased by 5, therefore, the new observations are :

The mean of above observation is given by

∴ The new mean also increases by 5 from the previous mean