Question

In a psychology class, 28 students have a mean score of 83.6 on a test. Then 25 more students take the test and their mean score is 68.8. What is the mean score of all of these students together? Round to one decimal place. mean of the scores of all the students =

Answer 1

The new mean would be given by:

`\bar X_f = (\sum_(i=1)^n X +X_1)/(28+25)`

And replacing we got:

`\bar X_f = (2340.8+ 1720)/(28+25)= 76.6`

Explanation:

We know that the original mean from the 28 students is given by:

`\bar X= (\sum_(i=1)^(28) X_i)/(28)= 83.6`

The sum of the values is:

`\sum_(i=1)^(28) X_i = 28*83.6 =2340.8`

And now we know that the new mean is 68.8 with the 25 new people so then the new mean would be given by:

`\bar X_1 = (\sum_(i=1)^(25) X_i)/(25) = 68.8`

The sum of the values is:

`\sum_(i=1)^(25) X_i = 25*68.8 =1720`

The new mean would be given by:

`\bar X_f = (\sum_(i=1)^n X +X_1)/(28+25)`

And replacing we got:

`\bar X_f = (2340.8+ 1720)/(28+25)= 76.6`