Question

In a group, 10 freshmen have mean GPA of 3.5; 20 sophomores have a mean GPA of 2.9; 25 juniors have a mean GPA of 3.2; and 15 seniors have a mean GPA of 3.4. What is the mean of the entire group

Answer 1

`T_1 = 10*3.5 = 35`

`T_2 = 20*2.9 = 58`

`T_3 = 25*3.2 = 80`

`T_4 = 15*3.4 = 51`

`\bar X= (T_1 +T_2 +T_3 +T_4)/(10+20+25+15)= (35+58+80+51)/(10+20+25+15) = 3.2`

Explanation:

For this case we have the following info given:

`n_1= 10 , \bar X_1 = 3.5` for freshmen

`n_2= 20 , \bar X_2 = 2.9` for sophomores

`n_3= 25 , \bar X_3 = 3.2` for juniors

`n_4= 15 , \bar X_4 = 3.4` for seniors

For this case we can use the formula for the sample mean in order to find the total of each group:

`\bar X =(\sum_(i=1)^n X_i)/(n)`

`T= \sum_(i=1)^n X_i = n *\bar X`

And replacing we got:

`T_1 = 10*3.5 = 35`

`T_2 = 20*2.9 = 58`

`T_3 = 25*3.2 = 80`

`T_4 = 15*3.4 = 51`

And the grand mean would be given by:

`\bar X= (T_1 +T_2 +T_3 +T_4)/(10+20+25+15)= (35+58+80+51)/(10+20+25+15) = 3.2`