Question

A group of 12 students has a mean height of 58 inches. Another group of 6 students has a mean height of 52 inches. What is the mean height of the 18 students? Explain how you found your answer.

Answer 1

The mean height of the 18 students = 56 inches

Explanation:

Given Data:

Group 1:

number of students = 12

Mean(x-bar) = 58 inches

Group 2:

number of students = 18

Mean(x-bar) = 52 inches

calculating the sum of the number of students in group 1, we have;

Mean(x-bar) = Σx/number of students

58 = Σx/12

Σx = 58*12

= 696

calculating the sum of the number of students in group 2, we have;

Mean(x-bar) = Σx/number of students

52 = Σx/6

Σx = 52*6

= 312

Calculating the mean of the 18 students, we have;

Mean(x-bar) = Σx/total number of students

= (696+312)/18

Σx = 1008/18

= 56 inches

Therefore, the mean height of the 18 students = 56 inches

Answer 2

56 inches

Explanation:

A weighted average must be made, that each average has an assigned weight and in this way a resulting average can be obtained.

That is, the average of 12 students has a weight of 12 and the average of 6 students has a weight of 6, and then divide by the total weight, that is, 18, like this:

(58*12 + 52*6) / 18 = 56

56 inches tall is the average of the 18 students