A student scored 60, 70, and 80 in three subjects with weights 2, 3, and 5, respectively. What is the weighted mean score?

To find the weighted mean score, we use the weighted mean formula, which accounts for the varying importance (weights) of each score. The weighted mean is calculated by summing the products of each score and its corresponding weight, and then dividing that sum by the total sum of the weights.

The formula for the weighted mean is:
$\text{Weighted Mean}=\frac{\sum (x_i·w_i)}{\sum w_i}$
where $x_i$ represents the scores and $w_i$ represents the weights.

Let's list the given values from the problem:
- First score ($x_1$) = 60 with weight ($w_1$) = 2
- Second score ($x_2$) = 70 with weight ($w_2$) = 3
- Third score ($x_3$) = 80 with weight ($w_3$) = 5

Step 1: Calculate the sum of the weighted scores (the numerator):
$\sum (x_i·w_i)=(60·2)+(70·3)+(80·5)$
$\sum (x_i·w_i)=120+210+400=730$

Step 2: Calculate the sum of the weights (the denominator):
$\sum w_i=2+3+5=10$

Step 3: Divide the sum of the weighted scores by the total weight:
$\text{Weighted Mean}=\frac{730}{10}=73$

Therefore, the weighted mean score is 73.