Answer to Question #119070 in Statistics and Probability for Harriet

Question

There are 20 people in a singing group. The mean age of 12 of the members is 18 years. The mean age of the remaining 8 is 23 years. What is the mean age of the 20 members of the singing group?

Answer 1

$$mean=\mu={\displaystyle\sum_{i=1}^nx_i\over n}$$

The mean age of 12 of the members is 18 years:

$$\mu_1={\displaystyle\sum_{i=1}^{12}x_i\over 12}=18$$

$$\displaystyle\sum_{i=1}^{12}x_i=12(18)=216$$

The mean age of the remaining 8 is 23 years:

$$\mu_2={\displaystyle\sum_{i=13}^{20}x_i\over 8}=23$$

$$\displaystyle\sum_{i=13}^{20}x_i=8(23)=184$$

What is the mean age of the 20 members of the singing group?

$$\mu={\displaystyle\sum_{i=1}^{20}x_i\over 20}={\displaystyle\sum_{i=1}^{12}x_i+\displaystyle\sum_{i=13}^{20}x_i\over 20}=$$

$$={216+184\over 20}=20$$

The mean age of the 20 members of the singing group is 20 years.