We are given a statistical series of two variables and the regression line equation $y = 9x + 0.6$. The goal is to calculate the mean of the $x_i$ values and then show that $t=20$.

1. Problem Description

We are given a statistical series of two variables and the regression line equation $y = 9x + 0.6$. The goal is to calculate the mean of the $x_i$ values and then show that $t=20$.

2. Solution Steps

First, we need to compute the mean $\bar{x}$ of the $x_i$ values. The values are 1.2, 1.4, 1.6, 1.8, and

2. So, we sum these values and divide by 5:

$$\bar{x} = \frac{1.2 + 1.4 + 1.6 + 1.8 + 2}{5} = \frac{8}{5} = 1.6$$

Next, we need to express $\bar{y}$ in terms of $t$. The $y_i$ values are 13, 12, 14, 16, and $t$. The mean $\bar{y}$ is given by:

$$\bar{y} = \frac{13 + 12 + 14 + 16 + t}{5} = \frac{55 + t}{5}$$

The point $(\bar{x}, \bar{y})$ lies on the regression line, so we have:

$$\bar{y} = 9\bar{x} + 0.6$$

Substituting the values we found for $\bar{x}$ and $\bar{y}$, we get:

$$\frac{55 + t}{5} = 9(1.6) + 0.6$$

$$\frac{55 + t}{5} = 14.4 + 0.6$$

$$\frac{55 + t}{5} = 15$$

$$55 + t = 15 \times 5$$

$$55 + t = 75$$

$$t = 75 - 55$$

$$t = 20$$

3. Final Answer

The mean of $x_i$ is $\bar{x} = 1.6$. And we showed that $t=20$.