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

Answer:

The mean of the total number of students is 85.5

Step-by-step explanation:

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

$\frac{\sum_{i=1}^n x_i}{n}$.

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

$\frac{\sum_{i=1}^{47} x_i}{47}$

REcall the following

$\frac{\sum_{i=1}^{24}x_i}{24} =86$

$\frac{\sum_{i=25}^{47}x_i}{23} =85$

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,

$\frac{\sum_{i=1}^{47} x_i}{47}= \frac{86\cdot 24 + 85\cdot 23}{47}= 85.5$