Measures of central tendency · Ages 14–15
Weighted mean
Σ(value × weight) ÷ Σweights.
How to do it
Method
Σ(value × weight) ÷ Σweights
(80 × 2 + 90 × 3) ÷ (2 + 3) = 86
Another way
As repeated values
The mean of 80, 80, 90, 90, 90 = 86
In full
When the parts don't count equally, use a weighted mean: multiply each by its weight, add, then divide by the sum of the weights. A game rated 80 for graphics (weight 2) and 90 for gameplay (weight 3): (80 × 2 + 90 × 3) ÷ (2 + 3) = 430 ÷ 5 = 86. A heavier weight counts for more, so the weighted mean sits nearer the heavier part (86 is nearer 90 than 85 is). Weights can be percentages: 40% graphics and 60% gameplay give 80 × 40% + 90 × 60% = 86, the weights making 100%, so no dividing. Or think of it like this: weights 2 and 3 are as if 80 came twice and 90 three times; the mean of 80, 80, 90, 90, 90 is the same.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A games review site rates a new game 71 for graphics, with weight 3, and 85 for gameplay, with weight 1. What is the weighted mean rating?
Show the answer and working
Answer: 74.5 points
Σ(rating × weight) ÷ Σweights = (71 × 3 + 85 × 1) ÷ (3 + 1) = 298 ÷ 4 = 74.5.
Example 2
A café's rating counts taste as 30% and service as 70%. It scores 58 for taste and 89 for service. What is its overall rating?
Show the answer and working
Answer: 79.7 points
The weights are percentages making 100%, so no dividing: 58 × 30% + 89 × 70% = 79.7.
Example 3
In a review, a phone scores 53 for looks (weight 1) and 63 for performance (weight 3). What is its weighted mean score?
- A. 58
- B. 55.5
- C. 121
- D. 60.5
Choose the right answer
Show the answer and working
Answer: D. 60.5
(53 × 1 + 63 × 3) ÷ (1 + 3) = 242 ÷ 4 = 60.5, nearer the heavier 63 than the plain mean 58 is.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.A café's rating counts taste as 80% and service as 20%. It scores 59 for taste and 53 for service. What is its overall rating?
Answer:
2.A games review site rates a new game 64 for graphics, with weight 2, and 70 for gameplay, with weight 3. What is the weighted mean rating?
Answer:
3.In a review, a phone scores 74 for looks (weight 1) and 98 for performance (weight 4). What is its weighted mean score?
- A. 86
- B. 93.2
- C. 233
- D. 78.8
Choose the right answer
Answer:
4.An e-bike's rating is a weighted mean: range 73 (weight 1) and looks 67 (weight 3). The new model's range score is 9 higher than the old one's, its looks score the same. By how much is the new model's weighted mean higher?
Answer:
5.In a diving contest, a dive's difficulty mark is 67 (weight 1) and its execution mark 88 (weight 2). Its weighted mean mark is 77.5.
True or false?
Answer:
All the answers
- 1. 57.8 points
- 2. 67.6 points
- 3. B. 93.2
- 4. 2.25 points
- 5. False
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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