Franciy Shoo
more than 1 week ago
Explain with example the mean of weighted average?
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ChatGPT
more than 1 week ago
A weighted average is a type of average where different values have different weights or importance. The weighted average is calculated by multiplying each value by its weight, summing up these products, and then dividing by the sum of the weights.
For example, let's say you have three exams in a class: Exam 1 is worth 20% of your grade, Exam 2 is worth 30% of your grade, and Exam 3 is worth 50% of your grade. Your scores on these exams are 80, 90, and 85 respectively.
To calculate your weighted average grade, you would multiply each exam score by its weight:
(80 * 0.20) + (90 * 0.30) + (85 * 0.50) = 16 + 27 + 42.5 = 85.5
So, your weighted average grade in the class is 85.5. This means that Exam 3, which is worth the most, has the biggest impact on your overall grade.
For example, let's say you have three exams in a class: Exam 1 is worth 20% of your grade, Exam 2 is worth 30% of your grade, and Exam 3 is worth 50% of your grade. Your scores on these exams are 80, 90, and 85 respectively.
To calculate your weighted average grade, you would multiply each exam score by its weight:
(80 * 0.20) + (90 * 0.30) + (85 * 0.50) = 16 + 27 + 42.5 = 85.5
So, your weighted average grade in the class is 85.5. This means that Exam 3, which is worth the most, has the biggest impact on your overall grade.
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Google Gemini AI
more than 1 week ago
What is a Weighted Average?
A weighted average is a calculation that produces an average value, but assigns different levels of importance to the individual values being averaged. Each value is multiplied by a weight, and these weighted values are then summed to obtain the weighted average.
Concept of Weights:
The weights represent the relative importance of each value in the average. They are typically positive numbers, but can also be negative. The sum of the weights must equal 1.
Formula:
```
Weighted Average = (Value1 - Weight1 + Value2 - Weight2 + ... + ValueN - WeightN) / (Weight1 + Weight2 + ... + WeightN)
```
Example:
Suppose you have test scores for three students and want to calculate their weighted average, where the weight represents the importance of the test:
- Student 1: Score = 85, Weight = 0.5
- Student 2: Score = 90, Weight = 0.3
- Student 3: Score = 95, Weight = 0.2
Weighted Average Calculation:
```
Weighted Average = ((85 - 0.5) + (90 - 0.3) + (95 - 0.2)) / (0.5 + 0.3 + 0.2)
```
```
Weighted Average = (42.5 + 27 + 19) / 1
```
```
Weighted Average = 88.5
```
Therefore, the weighted average of the test scores is 88.5.
Interpretation:
The weighted average assigns greater importance to Student 1's score, which has a weight of 0.5, compared to Student 2's and Student 3's scores, which have weights of 0.3 and 0.2, respectively. Consequently, Student 1's score contributes more significantly to the overall average than the other students'.
A weighted average is a calculation that produces an average value, but assigns different levels of importance to the individual values being averaged. Each value is multiplied by a weight, and these weighted values are then summed to obtain the weighted average.
Concept of Weights:
The weights represent the relative importance of each value in the average. They are typically positive numbers, but can also be negative. The sum of the weights must equal 1.
Formula:
```
Weighted Average = (Value1 - Weight1 + Value2 - Weight2 + ... + ValueN - WeightN) / (Weight1 + Weight2 + ... + WeightN)
```
Example:
Suppose you have test scores for three students and want to calculate their weighted average, where the weight represents the importance of the test:
- Student 1: Score = 85, Weight = 0.5
- Student 2: Score = 90, Weight = 0.3
- Student 3: Score = 95, Weight = 0.2
Weighted Average Calculation:
```
Weighted Average = ((85 - 0.5) + (90 - 0.3) + (95 - 0.2)) / (0.5 + 0.3 + 0.2)
```
```
Weighted Average = (42.5 + 27 + 19) / 1
```
```
Weighted Average = 88.5
```
Therefore, the weighted average of the test scores is 88.5.
Interpretation:
The weighted average assigns greater importance to Student 1's score, which has a weight of 0.5, compared to Student 2's and Student 3's scores, which have weights of 0.3 and 0.2, respectively. Consequently, Student 1's score contributes more significantly to the overall average than the other students'.
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