#### (i)The marks (out of 100) obtained by a group of students in a Mathematics test are 81, 72, 90, 90, 85, 86, 70, 93 and 71. Find the mean marks obtained by the group of students.

(ii) The mean of the age of three students Vijay, Rahul and Rakhi is 15 years. If their ages are in the ratio 4 :5:6 respectively, then find their ages.

**Solution:**

(i) The marks obtained by the group of students

81, 72, 90, 90, 85, 86, 70, 93, 71

Here, n = 9

∴ Mean (x̄) = Ʃ x_{i}/n

= (81 + 72 + 90 + 90 + 85 + 86 + 70 + 93 + 71)/9

= 738/9 = 82

Hence, the mean marks obtained by the group of students is 82.

(ii) the mean of the age of three students Vijay, Rahul and Rakhi is 15 years.

So, n = 3

Now, the sum of ages of the 3 students = 15×3 = 45

Also given, ratio of their ages is 4 : 5 : 6

Sum of ratios = 4 + 5 + 6 = 15

Hence,

Vijay’s age = (45/15)×4 = 12 years

Rahul’s age = (45/15)×5 = 15 years

Rakhi’s age = (45/15)×6 = 18 years

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