We are given the body masses of 6 students: 35, 40, 45, 45, 50, and $y^2$. The sample mean is 41. We need to find the value of $y^2$.

1. Problem Description

We are given the body masses of 6 students: 35, 40, 45, 45, 50, and $y^2$. The sample mean is

4

1. We need to find the value of $y^2$.

2. Solution Steps

The formula for the sample mean is:

$\text{mean} = \frac{\text{sum of values}}{\text{number of values}}$

We are given that the mean is 41, and the number of values is

6. So, $41 = \frac{35 + 40 + 45 + 45 + 50 + y^2}{6}$.

Multiplying both sides by 6, we get:

$41 \times 6 = 35 + 40 + 45 + 45 + 50 + y^2$

$246 = 215 + y^2$

Subtracting 215 from both sides, we get:

$y^2 = 246 - 215$

$y^2 = 31$

3. Final Answer

$y^2 = 31$