Question

student in two fifth grade classes were given the same english test. one class of 24 studmets had a mean 86, and the second class of 23 students had a mean of 85. what is the mean for the total number of students in both classes to the nearest 0.1

Answer 1

The mean of the total number of students is 85.5

Explanation:

REcall that given n data points
`x_1, \dots, x_n`, the mean is given by

`(\sum_(i=1)^n x_i)/(n)`.

Let us number the students of the 24 students' class from 1 to 24 and the let us number the students of the other class from 25 to 47.

The question is to find the following

`(\sum_(i=1)^(47) x_i)/(47)`

REcall the following

`(\sum_(i=1)^(24)x_i)/(24) =86`

`(\sum_(i=25)^(47)x_i)/(23) =85`

Then, from this equations we can deduce that

`\sum_(i=1)^(47)x_i = \sum_(i=1)^(24)x_i + \sum_(i=25)^(47)x_i = 86\cdot 24 + 85\cdot 23`

Therefore,

`(\sum_(i=1)^(47) x_i)/(47)= (86\cdot 24 + 85\cdot 23)/(47)= 85.5`