Question

The mean of 9 numbers is x. If one number is included which is 3x, then the new mean is

• A. $12+x$
• B. $1.2x$
• C. $12-x$
• D. $\frac{12}{x}$
  

Answer 1

The correct option is B $1.2x$

Given that the mean of 9 numbers is x.
$\therefore$ Mean = $\frac{\text{Sum of observations}}{\text{Total number of observations}}$
$\Rightarrow x=\frac{\text{Sum of 9 numbers}}{9}$
$\Rightarrow 9x=$ Sum of 9 numbers …..(i)
When a new number 3x is added, the new mean becomes:
New mean = $\frac{\left(\text{Sum of 9 numbers}\right)+3x}{10}$
$=\frac{9x+3x}{10}$ [From (i)]
$=\frac{12x}{10}$
$=1.2x$
Hence, the correct answer is option (b).