Question

if the average marks of four batches of 32 ,46,52 and 28 students respectively is 45 ,55,58 and 48 than average marks of all the student is?​

Answer 1

Average marks of all the student is 52.72 marks.

Step-by-step explanation:

We are given that the average marks of four batches of 32 ,46, 52 and 28 students respectively is 45 , 55, 58 and 48.

As we know that, Mean(Average) formula is given by;

                Mean  =  $\frac{\text{Total sum of all the observations}}{\text{Number of observations}}$

                                    Or

                       $\bar X =\frac{\sum X }{\text{n}}$

where, $\sum X$  =  Total sum of all observations in the data

                n  =  Number of observations

Also,  $\sum X$ = $\bar X \times n$

So, total sum of marks of first batch of 32 students =  $32 \times 45 =1440$

Total sum of marks of second batch of 46 students =  $46 \times 55 =2530$

Total sum of marks of third batch of 52 students =  $52 \times 58 =3016$

Total sum of marks of fourth batch of 28 students =  $28 \times 48 =1344$

Now, Total sum of marks of all batches of 158 students in class = 1440 + 2530 + 3016 + 1344 = 8330

And Total number of students in class = 32 + 46 + 52 + 28 = 158

Therefore, average mark of all the student =  $\frac{8330}{158}$

                                                                       =  52.72

Hence, the average mark of all the student is 52.72 marks.