Answer to Question #176841 in Statistics and Probability for alaa jeak

Question

Jacob's class organized a food drive he calculated the weighted mean for the average number of items collected per student

# of students 25,14,35,32,36,18

average #of items collected per student 4.4,3.0,4.8,5.5,5.5,5.0

Jacob calculated the weighted mean as follows: 4.4+3.0+4.8+5.5+5.5+5.0/6=4.7

what error did Jacob make?

what is the correct weighted mean

Answer 1

Jacob made an error because in his calculation he did not put into consideration the fact that the groups of students contained varying numbers of students and therefore contributing differently to the final mean. This is where weighted mean comes in

The correct weighted mean is calculated as follows:

Step 1 calculate the sum of the weights

25 + 14 + 35 + 32 + 36 + 18 = 160

Step 2 multiply each average by its weight then get the sum

$\frac{25}{160}\times4.4+\frac{14}{160}\times3.0+\frac{35}{160}\times4.8+\frac{32}{160}\times5.5+\frac{36}{160}\times5.5+\frac{18}{160}\times5.0$

= 0.69 + 0.26 + 1.05 + 1.1 + 1.24 + 0.56 = 4.9

Therefore weighted mean = 4.9