To calculate the weighted mean, you use the following formula:

$\text{Weighted Mean} = \frac{\sum (w_i \times x_i)}{\sum w_i}$

Where:

• $w_i$ is the weight of each data value
• $x_i$ is the corresponding data value
• The summation goes over all data points.

Given the data:

Weights:
4.98, 1.90, 4.26, 5.41, 2.36, 6.96, 4.92, 5.40

Data Values:
5, 6, 7, 2, 8, 8, 9, 6

Let's first calculate the weighted sum of the values:

$w_1 \times x_1 = 4.98 \times 5 = 24.90$ $w_2 \times x_2 = 1.90 \times 6 = 11.40$ $w_3 \times x_3 = 4.26 \times 7 = 29.82$ $w_4 \times x_4 = 5.41 \times 2 = 10.82$ $w_5 \times x_5 = 2.36 \times 8 = 18.88$ $w_6 \times x_6 = 6.96 \times 8 = 55.68$ $w_7 \times x_7 = 4.92 \times 9 = 44.28$ $w_8 \times x_8 = 5.40 \times 6 = 32.40$

Now, let's compute the weighted sum and the total weight:

$\text{Weighted sum} = 24.90 + 11.40 + 29.82 + 10.82 + 18.88 + 55.68 + 44.28 + 32.40 = 227.18$

$\text{Total weight} = 4.98 + 1.90 + 4.26 + 5.41 + 2.36 + 6.96 + 4.92 + 5.40 = 36.19$

Now, calculate the weighted mean:

$\text{Weighted Mean} = \frac{227.18}{36.19} \approx 6.278$

So, the weighted mean is approximately 6.278.

Would you like to dive deeper into the details of this calculation? Or do you have any other questions?

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Related Questions:

1. How would the calculation change if the data values were different?
2. What is the difference between a simple mean and a weighted mean?
3. How do you calculate the variance or standard deviation of a weighted dataset?
4. How would you interpret a weighted mean in real-life data analysis?
5. What happens if the weights are all equal?

Tip: When calculating weighted means, ensure that the weights and data points are aligned correctly, as a mismatch will skew the result.