Faculty Average Height Calculation
This problem requires us to find the overall average height of all faculty members at the university. We are given the total number of faculty, the percentage of females, and the average height for both females and males. We can solve this by calculating the total height contributed by females and males separately, summing them up, and then dividing by the total number of faculty.
Number of Male and Female Faculty
First, let's find out how many male and female faculty members there are.
- Total number of faculty = 750
- Percentage of females = 60%
- Number of female faculty = $60\%$ of $750 = 0.60 \times 750 = 450$
- Since faculty are only male and female, the percentage of males is $100\% - 60\% = 40\%$.
- Number of male faculty = $40\%$ of $750 = 0.40 \times 750 = 300$.
- Alternatively, Number of male faculty = Total faculty - Number of female faculty = $750 - 450 = 300$.
Total Height Calculation per Group
Next, we calculate the sum of heights for all females and all males.
- Average height of females = 162 cm
- Total height of all female faculty = (Number of females) $\times$ (Average height of females)
- Total height of females = $450 \times 162 \text{ cm} = 72900 \text{ cm}$
- Average height of males = 168 cm
- Total height of all male faculty = (Number of males) $\times$ (Average height of males)
- Total height of males = $300 \times 168 \text{ cm} = 50400 \text{ cm}$
Overall Average Faculty Height
Finally, we combine the total heights and divide by the total number of faculty to find the overall average height.
- Total height of all faculty = Total height of females + Total height of males
- Total height of all faculty = $72900 \text{ cm} + 50400 \text{ cm} = 123300 \text{ cm}$
- Total number of faculty = 750
- Overall average height = $\frac{\text{Total height of all faculty}}{\text{Total number of faculty}}$
- Overall average height = $\frac{123300 \text{ cm}}{750} = 164.4 \text{ cm}$
Final Average Height
The average height of the faculty of the university is 164.4 cm.
Important Questions from Average
The average height of 20 students of class 8 is 152 cm and the average height of 15 students of class 9 is 168 cm. What is the average height (to the nearest cm) of the students of both classes?
The average of 4, 6, 8, 12 and x is 7 and the average of x, 9, 13, 15 and y is 9. What is the value of 2x - 3y?
The average weight of 20 girls in a school was 52 kg. Two new students of weight 54 kg and 50 kg were admitted. The ratio of this new average to the old one is:
If the average of two numbers is 13 and the square root of their product is 12, then the difference between the numbers is:
If the average of 5 consecutive odd integers in increasing order is 11 , then the average of the last 3 of them is:
