The mean weight of 150 students in a class is 60kg the mean weight of boys is 70kg with a standard deviation of 10kg for the girls the mean weight is 55kg with a standard deviation of 15kg find the number of boys and girls in the class and the combined standard deviation
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Let the no. Of boys be x
and girls be y
Therefore x + y = 150 (given)
Since, Mean = Sum of observation / Total no. Of observation
= 70x +55y/x+y = 60
[Taking 5 common from both the sides]
Now we have two equations
1st: 14x + 11y =1800
2nd: x + y =150
Multiplying 2nd eq by 11 and simultaneous solving, we get
14x + 11y = 1800
11x + 11y = 1650
By subtracting y terms will be cancelled
⇒3x = 150 OR x = 50 Hence y = 150 - 50 = 100
and girls be y
Therefore x + y = 150 (given)
Since, Mean = Sum of observation / Total no. Of observation
= 70x +55y/x+y = 60
[Taking 5 common from both the sides]
Now we have two equations
1st: 14x + 11y =1800
2nd: x + y =150
Multiplying 2nd eq by 11 and simultaneous solving, we get
14x + 11y = 1800
11x + 11y = 1650
By subtracting y terms will be cancelled
⇒3x = 150 OR x = 50 Hence y = 150 - 50 = 100
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