The performance of a student in a business school was evaluated as follows. Calculate weighted mean from the given data and distinguish between weighted arithmetic mean and simple arithmetic mean. Marks Obtained Weights Class test Presentation Attendance Class participation Final examination 38 36 15 20 55 10 15 05 10 60
Answers
The performance of a student in a business school was evaluated as follows.
Given,
Marks Obtained Weights
Class test 38 10
Presentation 36 15
Attendance 15 05
Class participation 20 10
Final examination 55 60
Weighted mean = ∑ wi × xi / ∑ wi
= [ 38 × 10 + 36 × 15 + 15 × 5 + 20 × 10 + 55 × 60 ] / [ 10 + 15 + 5 + 10 + 60 ]
= [ 380 + 540 + 75 + 200 + 3300 ] / 100
= 4495 / 100
= 44.95
Therefore, the weighted mean is 44.95
Arithmetic mean = ∑ xi / N
= [ 38 + 36 + 15 + 20 + 55 ] / [ 10 + 15 + 5 + 10 + 60 ]
= 164 / 100
= 16.4
Therefore, the arithmetic mean is 16.4
In case of weighted mean, wi is the weight associated with the element xi and it represents the number of times that element appears in the data set.
In case of arithmetic mean, the elements of data set xi are directly divided by the total number of frequencies.