Question

If the sum of the deviations of $50$ observations from $30$ is $50$, then the mean of these observation is :

• A. 50
• B. 51
• C. 30
• D. 31

Answer 1

Answer: (D)

31

Answer 2

$\sum^{50}_{i=1} \left(x_{i} -30\right) =50$
$\sum x_{1} = 50 \times30 =50$
$\sum x_{1} =50 + 50 +30$
$\text{Mean} = \bar{x} = \frac{\sum x_{i}}{n} = \frac{50\times30+50}{50} = 30+1 = 31$