High School

Find the combined mean of two sets of data or calculate a new mean when extra data is added.

There are 25 women and 15 men in an office.
- The mean age of the women is 36.8.
- The mean age of the men is 39.4.

Work out the mean age of all 40 people.

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.

Other Questions