Question

If the mean of observation \[x_1 , x_2 , . . . . , x_n is x\]  then the mean of x₁ + a, x₂ + a, ....., x_n + a is 

विकल्प

• a`overlineX`

• `overlineX -a`

• `overlineX +a`

• `overlineX/a`

Answer 1

The mean of \[x_1 , x_2 , . . . , x_n\text {  is } \]`overlineX`.

\[\therefore \frac{x_1 + x_2 + x_3 + . . . + x_n}{n}\]  = `overlineX`

\[ \Rightarrow x_1 + x_2 + x_3 + . . . + x_n = n\]`overlineX`

Mean of x₁ + a, x₂ + a, ... , x_n + a

\[= \frac{\left( x_1 + a \right) + \left( x_2 + a \right) + \left( x_3 + a \right) + . . . + \left( x_n + a \right)}{n}\]

\[ = \frac{\left( x_1 + x_2 + x_3 + . . . + x_n \right) + \left( a + a + a + . . . + a \right)}{n}\]

`= (noverlineX + na)/n`

`= overlineX + a`