Question

Suppose that a class of 32 students has a mean test score of 75. The 17 male students in the class had a mean score of 60. What was the mean score for the 15 female students? (Use at least two decimals of accuracy when applicable)

Answer 1

The mean score for the 15 female students is 92.

Step-by-step explanation:

To find the mean score for the 15 female students, we can use the formula for the overall mean: (total sum of scores) / (total number of students). Since we know the mean score for the entire class (75) and the mean score for the male students (60), we can calculate the total sum of scores for the entire class by multiplying the class mean by the total number of students:

Total sum of scores = 75 * 32 = 2400.

Now, we subtract the sum of scores for the male students (mean score * number of male students) from the total sum of scores to find the sum of scores for the female students:

Sum of female scores = 2400 - (60 * 17) = 2400 - 1020 = 1380.

Finally, we calculate the mean score for the female students by dividing the sum of female scores by the number of female students (15):

Mean score for female students = 1380 / 15 = 92.

Answer 2

92

Step-by-step explanation:

Let x represent the mean test scores of each female student.

The total scores of 15 female students would be
`15x`.

We have been given that the 17 male students in the class had a mean score of 60.

The total scores of 17 male students would be
`17* 60=1020`.

We know that mean is equal to sum of data divided by total numbers in data set.

`\text{Average}=\frac{\text{Sum}}{\text{Count}}`

We are told that a class of 32 students has a mean test score of 75.

`75=(1020+15x)/(32)`

`75*32=(1020+15x)/(32)*32`

`2400=1020+15x`

`2400-1020=1020-1020+15x`

`1380=15x`

`(1380)/(15)=(15x)/(15)`

`92=x`

Therefore, the mean score for the 15 female students was 92.