The mean weight of five student is 51 kg and the mean weight of four students 54 kg.The mean weight of nine student will be ---Option 1.less than 52 kg 2.more than 53 3.between 52kg and 53kg

Dear Student,

Please find below the solution to the asked query:

We know :  Mean  = $\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations}}{\mathrm{Number} \mathrm{of} \mathrm{observations}}$

As given : The mean weight of five student is 51 kg , So

$\frac{\mathrm{Weight} \mathrm{of} 5 \mathrm{students}}{5}$ = 51  ,

Weight of 5 students =  255 kg                                --- ( 1 )

And given :  The mean weight of four students 54 kg , So

$\frac{\mathrm{Weight} \mathrm{of} 4 \mathrm{students}}{4}$ = 54  ,

Weight of 4 students =  216 kg                                --- ( 2 )

Now we add equation 1 and 2 and get :

Weight of 9 students =  471 kg

Then,

Mean weight of 9 students = $\frac{471}{9}$ = 52.33

And we can see that :  52 < 52.33 < 53

Therefore,

Option ( 3 )                                                        ( Ans )

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