Statistics Question, please help if you can

Question

1. 

Answer 1

Let s_n represent the score of student "n".

For class #1, the mean of 53 is calculated from (s₁ + s₂ + s₃ + . . . s₂₃)/23 so:

53 = (s₁ + s₂ + s₃ + . . . s₂₃)/23 or

(s₁ + s₂ + s₃ + . . . s₂₃) = 53•23 = 1219 (i.e., the total of all the student's scores in class #1 is 1219)

For class #2, the mean of 27 is calculated from (s₁ + s₂ + s₃ + . . . s₃₄)/34 so:

27 = (s₁ + s₂ + s₃ + . . . s₃₄)/34 or

(s₁ + s₂ + s₃ + . . . s₃₄) = 27•34 = 918

For class #3, the total of the scores is 45•25 = 1125. For class #4, the total of the scores is 85•32 = 2720. And for class #5, the total of the scores is 70•35 = 2450.

So the total of all scores is 1219 + 918 + 1125 + 2720 + 2450 = 8432. The total number of students is 23 + 34 + 25 + 32 + 35 = 149.

So the overall mean is 8432/149 = (approximately) 56.59

This is just a regular average (not weighted). To be a weighted average, you would need to apply some sort of a weighting factor to some scores that might make them "more important" than other scores. In this example, all scores are counted of equal "worth".

Answer 2

Mean of all classes = 53•23 + 27•34 + 45•25 + 85•32 + 70•35 / 23 +34 +25 +32 +35

= 1219 + 918 + 1125 + 2720 + 2450 / 149

= 8432 / 149

= 56·59

given information is of five classes , this is regular mean of five classes.