3. The weighted mean, denoted as is another measure of center in which weights c

Question

3. The weighted mean, denoted as is another measure of center in which weights can be associated with each of the individual obser- vations. The formula for the weighted mean is as follows w x 2 where w, is the weight associated with observation x Suppose an instructor counts examinations twice as much asquizzes, and counts the final examination three times as much as quizzes. If a student earned an average examination grade of 83, an average quiz grade of 87, and a final examination grade of 91, using the weighted mean, what would the student's average grade be? What would the student's grade be using the sample mean, X? Describe why there is a difference between these two values.

Explanation / Answer

Weighted mean xw

Average examination Grade = 83

Average Quiz Grade = 87

Final Examination Grade = 91

Lets say quiz is given weightage w, so so weightage of examinations weightage will be 2w and final examination weightage will be 3w.

Student average grade = xw = wi.xi / wi

= w * 87 + 2w * 83 + 3w * 91)/ (w + 2w + 3w) = 87.67

Sample mean x = (83 + 87 + 91)/3 = 87

There is differnce between these values as in weighted mean, variable are given diffeent-2 values but here in sample mean, every component is given only 1 value.

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