Page 67 - Mathematics of Business and Finance

Chapter 1 | Review of Basic Arithmetic 47

Example 1.5(e) Calculating the Weighted Average Solution (ii) Calculating the simple arithmetic average
continued
At a manufacturing organization, 15 employees are paid $20.00 per hour, 10 employees are paid d 35 + 30 + 40 + 95 n
$17.50 per hour, and 5 employees are paid $15.00 per hour. Calculate the weighted average hourly Arithmetic average = 50 50 50 100
rate of the employees. 4

Solution d 70 + 60 + 80 + 95 n
Wage Number of = 100
Wage Group Employees w x
(x ) (w ) i i 4
i
i
305
Group 1 $20.00 15 20 × 15 = 300 d 100 n
=
4
Group 2 $17.50 10 17.5 × 10 = 175
305
= × 100% = 76.25%
Group 3 $15.00 5 15 × 5 = 75 400
The simple arithmetic average does not reflect the importance given to the final examination.
Σw i = 30 Σw i x i = 550 The weighted average of 80% reflects the greater importance given to the final exam and,
therefore, it is the more suitable method in this situation.
n
/ w x 550
Using Formula 1.5(b), Weighted Average = i = 1 n i i = = 18.33333... = 18.33 Example 1.5(g) Calculating the Grade Point Average
/ w i 30
i = 1 Jean, a first semester student at the National College of Business, received the following first semester
Therefore, the weighted average hourly wage is $18.33. grades along with the credit earned per subject.

Subject Grade Credit Hours Earned
Example 1.5(f) Calculating the Weighted Average
English A 2
The final grade of a subject is determined by three tests and a final examination. Each test is worth
20% of the final grade and the final exam is worth 40%. A student received 35, 30, and 40 marks out Business Mathematics A 4
of 50 for the tests and 95 marks out of 100 for the final exam. Calculate the student's final grade for Marketing B 3
this subject based on: Computer Applications C 2
Accounting B 3
(i) The weighted average. (ii) The simple arithmetic average.
Business Management D 3
Which method is more suitable in this situation and why?
He planned to transfer to Hollings College of Business that required him to submit a Grade Point
Average (GPA) of his performance. The college uses the students' GPA to assess their overall academic
Solution (i) Calculating the weighted average
achievement. When calculating the GPA, the grade points for all courses are averaged, weighted by
credit hours. The school provided the following grade point conversion chart to calculate his GPA.
Value Weight
Terms of Terms of Terms w x
(x ) (w ) i i Grade Grade Point
i
i
35 35 A (80% to 100%) 4.0
Test 1 w = 20% 0.20 × = 14%
50 1 50 B (70% to 79%) 3.0
30 30
Test 2 w = 20% 0.20 × = 12% C (60% to 69%) 2.0
50 2 50
D (50% to 59%) 1.0
40 40
Test 3 w = 20% 0.20 × = 16% E (< 50%) 0
50 3 50
95 95 Based on the above information, calculate his GPA.
Final exam 100 w = 40% 0.40 × 100 = 38%
4
Σw = 100% Σw x = 80%
i
i i
n
/ w x 80%
Using Formula 1.5(b), Weighted Average = i = 1 n i i = = 80%
/ w i 100%
i = 1