Question

Period 1 has 15 students in it and a test average of 86%. Period 2 has 21 students in it and an average of 88%. Period 3 has 12 students in it and an average of 95%. Use weighted means to find the overall average of the classes

Answer 1

Add all of the percents up and then divide by 3. You get 89.6% 

Answer 2

The overall average of the classes is 89.125%

Explanation:

For calculate the average of the class using weighted means, it is necessary to take into account the number of students of every period. So, the average can be calculated as:

`Average =((x_1*a_1) +( x_2*a_2) + (x_3*a_3))/(x_1 + x_2 + x_3)`

Where is
`x_1, x_2` and
`x_3` are the number of students for period 1 , 2 and 3 respectively and
`a_1, a_2` and
`a_3` are the average of period 1, 2 and 3 respectively.

Replacing the values of x1 by 15 students, x2 by 21 students, x3 by 12 students, a1 by 86%, a2 by 88% and a3 by 95%, we get:

`Average = ((15*86)+(21*88)+(12*95))/(15+21+12)`

Average = 89.125%

So, using weighted means, the overall average of the classes is 89.125%