What is the mean weight of the remainder of the students if the mean weight of 15 students is 105 lbs, the mean weight of 5 of them is 100 lbs, and the mean weight of another 5 is 115 lbs?

Question

High School

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Answer :

EmmaGraceJohnson EmmaGraceJohnson · Answer 1 · 2024-12-09T13:17:56-05:00

To find the mean weight of the remainder of the students, we need to follow these steps:

Calculate the total weight of all 15 students.
Given that the mean weight of 15 students is 105 lbs, we can calculate the total weight by multiplying the mean by the number of students:
[tex]\text{Total weight of 15 students} = 105 \times 15 = 1575 \text{ lbs}[/tex]
Calculate the total weight of the first group of 5 students.
The mean weight of these 5 students is 100 lbs, so:
[tex]\text{Total weight of first 5 students} = 100 \times 5 = 500 \text{ lbs}[/tex]
Calculate the total weight of the second group of 5 students.
The mean weight of the next 5 students is 115 lbs:
[tex]\text{Total weight of second 5 students} = 115 \times 5 = 575 \text{ lbs}[/tex]
Calculate the total weight of the remaining 5 students.
Subtract the total weight of the first and second groups from the total weight of all 15 students:
[tex]\text{Total weight of remaining students} = 1575 - 500 - 575 = 500 \text{ lbs}[/tex]
Calculate the mean weight of the remaining students.
Since the remaining students are also 5 in number:
[tex]\text{Mean weight of remaining students} = \frac{500}{5} = 100 \text{ lbs}[/tex]

Therefore, the mean weight of the remainder of the students is 100 lbs.