The mean age of a group of 50 students is 15 years and the mean age of another group of 70 students is 20 yrs. Find the mean age of all the 120 students together.

Fundamentals of Mathematical Statistics (BCA) 1st Sem Previous Year Solved Question Paper 2022

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The mean age of a group of 50 students is 15 years and the mean age of another group of 70 students is 20 yrs. Find the mean age of all the 120 students together.

Explanation

Mean = (Total Sum of Ages) / (Total Number of Students)

the sum of ages for each group:

For the first group of 50 students with a mean age of 15 years:
Sum of Ages in Group 1 = 50 students * 15 years/student = 750 years

For the second group of 70 students with a mean age of 20 years:
Sum of Ages in Group 2 = 70 students * 20 years/student = 1400 years
the total sum of ages for all 120 students together:

Total Sum of Ages = Sum of Ages in Group 1 + Sum of Ages in Group 2
Total Sum of Ages = 750 years + 1400 years = 2150 years

the mean age of all 120 students together:

Mean = Total Sum of Ages / Total Number of Students
Mean = 2150 years / 120 students ≈ 17.92 years

So, the mean age of all 120 students together is approximately 17.92 years.

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