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Answer :
To find the mean age of all 40 people in the office, we need to combine the data from the 25 women and 15 men:
1. Identify the number of individuals and their mean ages:
- There are 25 women with a mean age of 36.8 years.
- There are 15 men with a mean age of 39.4 years.
2. Calculate the total age for each group:
- For the women: Multiply the mean age by the number of women.
[tex]\[
\text{Total age of women} = 25 \times 36.8
\][/tex]
This gives us a total age of approximately 920.
- For the men: Multiply the mean age by the number of men.
[tex]\[
\text{Total age of men} = 15 \times 39.4
\][/tex]
This gives us a total age of 591.
3. Combine the total ages:
- Add the total age for women and men to find the combined total age.
[tex]\[
\text{Total combined age} = 920 + 591
\][/tex]
This equals 1511.
4. Calculate the mean age of all individuals:
- Divide the total combined age by the total number of people.
[tex]\[
\text{Mean age} = \frac{1511}{40}
\][/tex]
This results in a mean age of approximately 37.775.
Therefore, the mean age of all 40 people in the office is around 37.775 years.
1. Identify the number of individuals and their mean ages:
- There are 25 women with a mean age of 36.8 years.
- There are 15 men with a mean age of 39.4 years.
2. Calculate the total age for each group:
- For the women: Multiply the mean age by the number of women.
[tex]\[
\text{Total age of women} = 25 \times 36.8
\][/tex]
This gives us a total age of approximately 920.
- For the men: Multiply the mean age by the number of men.
[tex]\[
\text{Total age of men} = 15 \times 39.4
\][/tex]
This gives us a total age of 591.
3. Combine the total ages:
- Add the total age for women and men to find the combined total age.
[tex]\[
\text{Total combined age} = 920 + 591
\][/tex]
This equals 1511.
4. Calculate the mean age of all individuals:
- Divide the total combined age by the total number of people.
[tex]\[
\text{Mean age} = \frac{1511}{40}
\][/tex]
This results in a mean age of approximately 37.775.
Therefore, the mean age of all 40 people in the office is around 37.775 years.
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