mean weight of 13 students In a class is 45 kg mean weight of first 7 students is 47 kg last 7 students is 43 kg find the weight of 7th student
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I'll give you two approaches to answer this question. The first approach is how I would answer this in a school assignment or examination. The second approach is how I would find the answer quickly in my mind:
First approach:
Recalling this definition:
Mean=TotalNumber of samplesMean=TotalNumber of samples
Use this on all the numbers you see in the question and you get enough material to find the answer.
Mean weight of students (M)=Total weight of students (W)Number of students (N)Mean weight of students (M)=Total weight of students (W)Number of students (N)
Mean weight of boys (Mb)=Total weight of boys (Wb)Number of boys (Nb)Mean weight of boys (Mb)=Total weight of boys (Wb)Number of boys (Nb)
Mean weight of girls (Mg)=Total weight of girls (Wg)Number of girls (Ng)Mean weight of girls (Mg)=Total weight of girls (Wg)Number of girls (Ng)
So we get
60=W15060=W150
70=WbNb70=WbNb
55=WgNg=W−Wb150−Nb55=WgNg=W−Wb150−Nb
So we get three linear equations with three variables, WW, WbWb, NbNb to solve for. I'll let you complete the rest for your assignment.
Second approach:
To quickly work it out in my mind, I would actually use a different approach. Unfortunately, my experience with using such ways in answering math questions at school has been poor. So I don't know if I can recommend this method for school assignments.
Look at the numbers closely:
55 kg55 kg (mean weight of girls)
60 kg60 kg (mean weight of all students)
70 kg70 kg (mean weight of boys)
I can quickly deduce that the number of girls is double the number of boys, because 60 kg60 kg is 5 kg5 kg away from 55 kg55 kg, and 10 kg10 kg way from 70 kg70 kg.
Since the total number of students is 150150, I know it has to be 100100 girls and 5050 boys.
This approach works because of the following relation:
Mb−MM−Mg=NbNgMb−MM−Mg=NbNg
You can prove this relation if you use:
M=NbMb+NgMgNb+Ng
First approach:
Recalling this definition:
Mean=TotalNumber of samplesMean=TotalNumber of samples
Use this on all the numbers you see in the question and you get enough material to find the answer.
Mean weight of students (M)=Total weight of students (W)Number of students (N)Mean weight of students (M)=Total weight of students (W)Number of students (N)
Mean weight of boys (Mb)=Total weight of boys (Wb)Number of boys (Nb)Mean weight of boys (Mb)=Total weight of boys (Wb)Number of boys (Nb)
Mean weight of girls (Mg)=Total weight of girls (Wg)Number of girls (Ng)Mean weight of girls (Mg)=Total weight of girls (Wg)Number of girls (Ng)
So we get
60=W15060=W150
70=WbNb70=WbNb
55=WgNg=W−Wb150−Nb55=WgNg=W−Wb150−Nb
So we get three linear equations with three variables, WW, WbWb, NbNb to solve for. I'll let you complete the rest for your assignment.
Second approach:
To quickly work it out in my mind, I would actually use a different approach. Unfortunately, my experience with using such ways in answering math questions at school has been poor. So I don't know if I can recommend this method for school assignments.
Look at the numbers closely:
55 kg55 kg (mean weight of girls)
60 kg60 kg (mean weight of all students)
70 kg70 kg (mean weight of boys)
I can quickly deduce that the number of girls is double the number of boys, because 60 kg60 kg is 5 kg5 kg away from 55 kg55 kg, and 10 kg10 kg way from 70 kg70 kg.
Since the total number of students is 150150, I know it has to be 100100 girls and 5050 boys.
This approach works because of the following relation:
Mb−MM−Mg=NbNgMb−MM−Mg=NbNg
You can prove this relation if you use:
M=NbMb+NgMgNb+Ng
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