JEE MAIN - Mathematics (2019 - 12th January Morning Slot - No. 1)
If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is :
31
50
51
30
Explanation
$$\sum\limits_{i = 1}^{50} {\left( {{x_i} - 30} \right) = 50} $$
$$\sum {{x_i}} = 50 \times 30 = 50$$
$$\sum {{x_i}} = 50 + 50 + 30$$
Mean $$ = \overline x = {{\sum {{x_i}} } \over n} = {{50 \times 30 + 50} \over {50}}$$
$$ = 30 + 1 = 31$$
$$\sum {{x_i}} = 50 \times 30 = 50$$
$$\sum {{x_i}} = 50 + 50 + 30$$
Mean $$ = \overline x = {{\sum {{x_i}} } \over n} = {{50 \times 30 + 50} \over {50}}$$
$$ = 30 + 1 = 31$$
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