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

1. Problem Description

The problem provides a dataset of body masses of 6 students: 35, 40, 45, 45, 50, and $y^2$. The sample mean is given as

4

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

2. Solution Steps

The sample mean is calculated by summing all the values in the dataset and dividing by the number of values. In this case, we have:

$Mean = \frac{35 + 40 + 45 + 45 + 50 + y^2}{6}$

We are given that the mean is

4

1. So,

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

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

$246 = 215 + y^2$

$y^2 = 246 - 215$

$y^2 = 31$

3. Final Answer

$y^2 = 31$