reasoning the table shows the daily changes in the barometric pressure (in inches of mercury) for four…

Explanation:

Step1: Recall the mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points.

Step2: Identify the data for part a

We have data for 4 days: $x_1=-0.05$, $x_2 = 0.09$, $x_3=-0.04$, $x_4=-0.08$, and $n = 4$.

Step3: Calculate the sum for part a

$\sum_{i = 1}^{4}x_{i}=-0.05 + 0.09-0.04-0.08=-0.08$.

Step4: Calculate the mean for part a

$\bar{x}=\frac{-0.08}{4}=-0.02$.

Step5: Set up an equation for part b

Let the change on Friday be $x$. We know that $n = 5$ (Monday - Friday) and the mean $\bar{x}=-0.01$. The sum of the first 4 values is $-0.08$ (from Step 3). Using the mean formula $\bar{x}=\frac{-0.08 + x}{5}$.

Step6: Solve the equation for part b

Since $\bar{x}=-0.01$, we have $-0.01=\frac{-0.08 + x}{5}$. Cross - multiply: $-0.01\times5=-0.08 + x$. So, $-0.05=-0.08 + x$. Then $x=-0.05 + 0.08=0.03$.

Answer:

a. $-0.02$ b. $0.03$