Page 66 - Mathematics of Business and Finance

46 Chapter 1 | Review of Basic Arithmetic

Example 1.5(e) Calculating the Weighted Average
At a manufacturing organization, 15 employees are paid $20.00 per hour, 10 employees are paid
$17.50 per hour, and 5 employees are paid $15.00 per hour. Calculate the weighted average hourly
rate of the employees.

Solution
Wage Number of
Wage Group Employees w x
(x ) (w ) i i
i
i
Group 1 $20.00 15 20 × 15 = 300

Group 2 $17.50 10 17.5 × 10 = 175

Group 3 $15.00 5 15 × 5 = 75

Σw i = 30 Σw i x i = 550

n
/ w x 550
Using Formula 1.5(b), Weighted Average = i = 1 n i i = = 18.33333... = 18.33
/ w i 30
i = 1
Therefore, the weighted average hourly wage is $18.33.

Example 1.5(f) Calculating the Weighted Average
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
of 50 for the tests and 95 marks out of 100 for the final exam. Calculate the student's final grade for
this subject based on:
(i) The weighted average. (ii) The simple arithmetic average.

Which method is more suitable in this situation and why?

Solution (i) Calculating the weighted average

Value Weight
Terms of Terms of Terms w x
(x ) (w ) i i
i
i
35 35
Test 1 w = 20% 0.20 × = 14%
50 1 50
30 30
Test 2 w = 20% 0.20 × = 12%
50 2 50
40 40
Test 3 w = 20% 0.20 × = 16%
50 3 50
95 95
Final exam 100 w = 40% 0.40 × 100 = 38%
4
i i
Σw i = 100% Σw x = 80%
n
/ w x 80%
Using Formula 1.5(b), Weighted Average = i = 1 n i i = = 80%
/ w i 100%
i = 1