The mean of ages of a group of 35 school students is 16 years. A 52 year old teacher joined the group. Find the mean of the ages of the students and the teacher.

Number of students = 35

Mean age of students = 16 years

Age of the teacher = 52 years

​$$\text{New Mean} = \frac{\text{Total Sum of Ages + Age of Teacher}}{\text{Total Number of Students + 1}}$$​​

Total Sum of Ages of students = Mean × Number of Students = 16 × 35 = 560

Total Sum of Ages (with teacher) = 560 + 52 = 612

Now,

New Mean = $$\frac{612}{35 + 1} = \frac{612}{36}$$​ = 17

Thus, The mean age of the students and the teacher is 17 years.