If arithmetic mean of weights of 100 students in class is 52 kgs. Out of 100 students there are 60 boys and arithmetic mean of their weight is 54 kgs. What is the arithmetic mean of weights of 40 girls ?
Answers
Step-by-step explanation:
If assume mean of weights of 40 girls is X,
52= 60*52 + 40*X
60+40
52= 3120 + 40 X
100
52*100= 3120 + 40 X
5200= 3120 + 40 X
5200- 3120 = 40X
1990 = 40X
40 40
49.75 = X
Given:
The arithmetic mean of weights of 100 students in class= 52 kg
The arithmetic mean of weights of 60 boys=54 kg
To find:
The arithmetic mean of weights of 40 girls
Solution:
The arithmetic mean of weights of 40 girls is 49 kg.
We can find the value by following the given steps-
We know that the mean of the weight of students can be obtained by dividing the sum of weights of all students by the total number of students.
The total number of students in class=100
Arithmetic mean of 100 students in class=52kg
Let the sum of the weights of all the students in the class be S kg.
So, the arithmetic mean of weights of all students in class= Sum of the weight of all students/ Total number of students in class
On putting the values, we get
52=S/100
52×100=S
S=5,200 kg
Sum of weights of all students in class=5,200kg
We also know that the number of boys in class=60
The arithmetic mean of weights of all boys in class=54kg
Let the sum of the weight of all the boys in the class be B kg.
Again, putting the values, we get
54=B/60
54×60=B
B=3,240kg
Now, the number of girls in class=40
The total weight of all the girls in class= Total weight of all the students in the class (S) - total weight of all the boys in the class (B)
=5,200-3,240
=1,960kg
So, the arithmetic mean of the weight of 40 girls=Sum of the weight of all girls/ Total number of girls in class
Arithmetic mean of weights of 40 girls=1,960/40
=196/4
=49 kg
Therefore, the arithmetic mean of weights of 40 girls is 49 kg.