Question

Arithmetic mean of marks (out of 25) scored by 10 students was 15. One of the student, named Karishma enquired the other 9 students and find the deviations from her marks are noted as – 8, – 6, – 3, – 1, 0, 2, 3,4, 6. Find Karishma’s marks.

Answer 1

Average marks of 10 students = 15 

Total marks of 10 students = 10 × 15 = 150 

Marks obtained by Karishma = x say 

Deviations of 9 students = -8, -6,-3,-1,0, 2, 3,4,6 

∴ x-8 + x-6 + x-3 + x-l + x + x + 2 + x + 3 + x + 4 + x + 6 + x = 150 

⇒ 10x- 3 = 150 

⇒ 10x = 150 + 3 = 153

x = 153/10 = 15.3

(Or)

The given observations are -8,-6,-3,-1,0, 2, 3, 4,6 

Let the number of marks of Karishma = 

Her deviation from x’ are – 8 + x, – 6 + x, – 3 + x, – 1 + x, x + 0, 2 + x, 3 + x, 4 + x, 6 + x

∴ Mean = Sum of  observations / Number of observations

[ ∵ Mean = 15 is given] 

10x – 3 = 15 × 10 

10x =150 + 3 

10x= 153 

x = 153/10

x = 15.3 

∴ Number of marks obtained by Karishma = 15.3