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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?

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    $\begingroup$ There's no way to calculate the employees average mean age without knowing the age of the woman who was replaced!!! $\endgroup$ – barak manos Apr 27 '15 at 12:22
  • $\begingroup$ @barakmanos: maybe we have to assume it is a number between $0$ and $39.2\cdot 59=2312.8$ :D $\endgroup$ – Jack D'Aurizio Apr 27 '15 at 12:26
  • $\begingroup$ The question is unclear. You didn't state if the $23$ year old man who replaced the $47$ year old woman was already working there or if it is a "new" employee. You state $91$ employees at the beginning but it is not clear if there are $91$ or $90$ after the replacement. $\endgroup$ – David Apr 27 '15 at 13:08
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Total men age is $32\cdot48.5+23=1575$

Total women age is $59\cdot39.2-47=2265.8$

Average age is therefore $\frac{1575+2265.8}{32+1+59-1}\approx42.2$

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  • $\begingroup$ Not after one new man comes and one woman leaves. $\endgroup$ – 5xum Apr 27 '15 at 12:57
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    $\begingroup$ @5xum: I've already taken that into consideration. $\endgroup$ – barak manos Apr 27 '15 at 12:58
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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 $f$.

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  • $\begingroup$ @hunter I expanded my answer, in which I explained just that. $\endgroup$ – 5xum Apr 27 '15 at 12:28
  • $\begingroup$ Sorry, forgot to write that the woman is 47 years old. $\endgroup$ – Math is fun Apr 27 '15 at 12:48
  • $\begingroup$ @Mathisfun Well then, my answer should have all the information you need! Just substitute $f=47$! $\endgroup$ – 5xum Apr 27 '15 at 12:56
  • $\begingroup$ Thanks but what does i stand for? @5xum $\endgroup$ – Math is fun Apr 27 '15 at 12:58
  • $\begingroup$ @Mathisfun It's jsut a sumation, so $\sum_{i=1}^{32} m_i$ simply means $m_1+m_2+\dots + m_{32}$. You read it as "the sum of all $m_i$ when $i$ goes from $1$ to $32$". You can even replace the sum with just a variable, $s_m$, the point is that the sum of all male ages (before hiring the new guy) can be calculated from the equation $\frac{s_m}{32} = 48.5$ $\endgroup$ – 5xum Apr 27 '15 at 13:00

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