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# If the sum of the deviations of 50 observations

Question:

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

1. 50

2. 51

3. 30

4. 31

Correct Option: , 4

Solution:

$\sum_{i=1}^{50}\left(x_{i}-30\right)=50$

$\Sigma x_{i}=50 \times 30=50$

$\Sigma x_{i}=50+50+30$

Mean $=\bar{x}=\frac{\sum x_{i}}{n}=\frac{50 \times 30+50}{50}=30+1=31$