In a company there are 32 men and 59 women. Male mean age is 48.5 and female 39.2. One of the women (47 years old) ended working at the company and was replaced with a 23 year old man.
Calculate the employees average mean age.
32 men + 59 women = 91 employees.
48.5+39.2=87.7 (age)
87.7/91= 0,96. Where am I doing wrong?
On
First of all, an important thing is that it is impossible to know the answer unless you know the age of the woman that stopped working.
The total age is not $48.5 + 39.2$. That is just the sum of two ages. In fact, $48.5$ is the mean age of all male employees, i.e. before the replacement, there are $32$ men with an average age of $48.5$, so if $s$ is the sum of all male ages, then $\frac{s}{32} = 48.5$. Same goes for women.
My advice is that you should, as you thought, find the sum of all ages in the company. It may be easier to actually number them, i.e. write down the male ages: $m_1,m_2,\dots, m_{32}$ and the female ages $f_1,\dots, f_{59}$.
Now, you know that the average age of the men is $$\frac{\sum_{i=1}^{32} m_i}{32} = 48.5$$
and you know that
$$\frac{\sum_{i=1}^{59} f_i}{59} = 39.2$$
Now, you also know that one more male is added, his age is $23$, and one female stoped working, let her age be $f$.
Now, you want the average age of the employees, which is
$$\frac{((\sum_{i=1}^{32} m_i) + 23) + ((\sum_{i=1}^{59} f_i) - f)}{59+32}$$
As you can see, this cannot be calculated without knowing $f$.
Total men age is $32\cdot48.5+23=1575$
Total women age is $59\cdot39.2-47=2265.8$
Average age is therefore $\frac{1575+2265.8}{32+1+59-1}\approx42.2$