Question

1. Calculate the weighted averages for two additional used cars using the weights given in the table below.

	New weights		Car 4 Ratings	Car 5 Ratings
Reliability	5		7	6
Gas Mileage	6		5	7
Interior Features/Comfort	10		8	7
Cargo Space	4		6	8

Make sure that you fill in each answer area before checking "How Did I Do?".

1. Weighted average for Car 4:  
2. Weighted average for Car 5:   

• In your weighted average equations in the problem above, how many total weights are used?
  
  
  
• For each category, what percent of the total weights are represented by the category weights? Enter your answers in the table.
  

  	New Weights as a Percentage of Total Weights
  Reliability	%
  Gas Mileage	%
  Interior Features/Comfort	%
  Cargo Space	%

  
  
• In the tables below, multiply each category’s percentage weight by its rating, and add up the four amounts.
  

  	Percentage Weights (written as a decimal)		Car 4 Ratings
  Reliability		×	7	=
  Gas Mileage		×	5	=
  Interior Features/Comfort		×	8	=
  Cargo Space		×	6	=
  Total

  
  
  

  	Percentage Weights (written as a decimal)		Car 5 Ratings
  Reliability		×	6	=
  Gas Mileage		×	7	=
  Interior Features/Comfort		×	7	=
  Cargo Space		×	8	=
  Total

  
  
• Write an equation for the weighted average using the percentage weights as decimals. Use the following variables to represent the individual rating in each category: R= Reliability; G= Gas Mileage; I= Interior Features/Comfort; C= Cargo Space.
  
  Weighted average =

Answer 1

Weighted average can be calculated as the Sum of the product of individual weights and Ratings and divide the result by the total number of individual weights.

Substituting the values For Car4, we get:

(7*5 + 5*6 + 8*10 + 6*4)/4 = (35 + 30 + 80 + 24)/4 = (169)/4 = 42.25

Hence, The weighted average for Car 4 is 42.25

Similarly, for Car 5, we get:

(6*5 + 7*6 + 7*10 + 8*4)/ = (30 + 42 + 70 + 32)/ 4 = (164)/4 = 41.00

Hence The weighted average for Car 5 is 41.00

To calculate the weights as a result of percentage of total weights, first you require the sum of all new weights:

5 + 6 + 10 + 4 = 25

Hence the total weight is 25.

We can now find the percentage of each individual weight against the total weight:

Reliability = (weight of reliability) / (total weight) * 100 = 5 / 25 * 100 = 0.20 = 20%

Calculating this for all weights, we get:

Reliability	20%
Gas mileage	24%
Interior Features/comfort	40%
Cargo space	16%

Using the above calculated percentages, we can fill the third table (for Car 4) as:

	Percentage Weights (written in decimal)		Car 4 rating
Reliability	0.20	x	7	=	1.4
Gas mileage	0.24	x	5	=	1.2
Interior Features/comfort	0.4	x	6	=	2.4
Cargo space	0.16	x	6	=	0.96
Total					5.96

Similarly the table for Car 5,

	Percentage Weights (written in decimal)		Car 5 rating
Reliability	0.20	x	6	=	1.2
Gas mileage	0.24	x	7	=	1.68
Interior Features/comfort	0.40	x	7	=	2.8
Cargo space	0.16	x	8	=	1.28
Total				=	6.96

In general, the formula for finding the weighed average using percentage as decimals would be:

Weighted average = R*0.20 + G*0.24 + I*0.40 + C*0.16