Question

If a 12-student class averaged 90 on a test, and a 20-student class averaged 80 on the test, then all 32 students averaged

Answer 1

Let the marks of the students in class 1 be

$m_1, m_2, ....., m_1_2$

the average of these 12 marks is 90, so 

$\frac{m_1+ m_2+ .....+ m_1_2}{12}=90$

which means

$m_1+ m_2+ .....+ m_1_2=90*12=1080$


similarly, let $n_1, n_2, ....., n_2_0$ be the marks of the students in the second class, 

so $\frac{n_1+ n_2+ ..... n_2_0}{20}=80$

which means $n_1+ n_2+ ..... n_2_0=80*20=1600$


The 32 students averaged:

$\frac{(m_1+ m_2+ .....+ m_1_2)+(n_1+ n_2+ ..... n_2_0)}{12+20}= \frac{1080+1600}{32}= \frac{2680}{32}= 83.75$

Answer 2

The formula to find the average of a data is given as follow
Mean = The sum of the data value ÷ Number of data

We would need the sum of 32 values to work out the mean score of 32 students. We will work out separately by finding the sum of scores of 12 students and sum of scores of 20 students

90 = Sum of data ÷ 12
Sum of data = 90×12 = 1080 scores

80 = Sum of data ÷ 20
Sum of data = 80×20 = 1600 scores

The sum of data of 32 students is 1080+1600 = 2680 scores
Mean = 2680÷32 = 83.75