Question
How to find weighted mean score
Answers
GPT-4o mini
To find the weighted mean (or weighted average) score, you need to follow these steps:
1. **Identify the Values**: Determine the values (scores) you want to average. Let’s denote these as \( x_1, x_2, x_3, \ldots, x_n \).
2. **Identify the Weights**: Determine the weights corresponding to each value. Denote the weights as \( w_1, w_2, w_3, \ldots, w_n \). Each weight represents the importance or frequency of the respective value.
3. **Calculate the Weighted Mean**: Use the formula for the weighted mean:
\[
\text{Weighted Mean} = \frac{\sum_{i=1}^{n} (x_i \cdot w_i)}{\sum_{i=1}^{n} w_i}
\]
Where:
- \( \sum_{i=1}^{n} (x_i \cdot w_i) \) is the sum of each score multiplied by its corresponding weight.
- \( \sum_{i=1}^{n} w_i \) is the sum of all weights.
### Example
Let's say you have the following scores and weights:
- Scores: \( x_1 = 80, x_2 = 90, x_3 = 70 \)
- Weights: \( w_1 = 1, w_2 = 2, w_3 = 1 \)
**Step 1: Calculate the weighted sum of the scores:**
\[
\text{Weighted Sum} = (80 \cdot 1) + (90 \cdot 2) + (70 \cdot 1) = 80 + 180 + 70 = 330
\]
**Step 2: Calculate the sum of the weights:**
\[
\text{Sum of Weights} = 1 + 2 + 1 = 4
\]
**Step 3: Calculate the weighted mean:**
\[
\text{Weighted Mean} = \frac{330}{4} = 82.5
\]
So, the weighted mean score is **82.5**.
1. **Identify the Values**: Determine the values (scores) you want to average. Let’s denote these as \( x_1, x_2, x_3, \ldots, x_n \).
2. **Identify the Weights**: Determine the weights corresponding to each value. Denote the weights as \( w_1, w_2, w_3, \ldots, w_n \). Each weight represents the importance or frequency of the respective value.
3. **Calculate the Weighted Mean**: Use the formula for the weighted mean:
\[
\text{Weighted Mean} = \frac{\sum_{i=1}^{n} (x_i \cdot w_i)}{\sum_{i=1}^{n} w_i}
\]
Where:
- \( \sum_{i=1}^{n} (x_i \cdot w_i) \) is the sum of each score multiplied by its corresponding weight.
- \( \sum_{i=1}^{n} w_i \) is the sum of all weights.
### Example
Let's say you have the following scores and weights:
- Scores: \( x_1 = 80, x_2 = 90, x_3 = 70 \)
- Weights: \( w_1 = 1, w_2 = 2, w_3 = 1 \)
**Step 1: Calculate the weighted sum of the scores:**
\[
\text{Weighted Sum} = (80 \cdot 1) + (90 \cdot 2) + (70 \cdot 1) = 80 + 180 + 70 = 330
\]
**Step 2: Calculate the sum of the weights:**
\[
\text{Sum of Weights} = 1 + 2 + 1 = 4
\]
**Step 3: Calculate the weighted mean:**
\[
\text{Weighted Mean} = \frac{330}{4} = 82.5
\]
So, the weighted mean score is **82.5**.