The arithmetic mean of marks scored by 10 students was 20. Nikhil, one of the students, inquired other 9 students and recorded their deviation from his marks as -5, 6, 2, -2, 0, 2, 4, -3, 6. Find the marks of Nikhil.

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Solution

The correct option is A 19
As we know,

Arithmetic mean = Estimated mean + Average of deviations

$A r i t h m e t i c m e a n = E s t i m a t e d m e a n + \frac{Sum of deviations}{Number of Observations}$

Let the marks of Nikhil = x.

As per the respective values given in question:

20 = x + $\frac{-5+6+2-2+0+2+4-3+6+0}{10}$

20 = x + $\frac{10}{10}$
20 = x + 1
x = 19

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The following table gives the marks obtained by $100$ students in a class test.

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Number of Students	$12$	$18$	$27$	$20$	$17$	$6$

Find the mean marks scored by a student in class test.

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