To answer your question and perform the necessary calculations using Desmos, let me guide you through the process. The task asks for the following:

1. Mean of $x$ and $y$ (denoted as $\bar{x}$ and $\bar{y}$).
2. Standard deviations of $x$ and $y$ (denoted as $SD_x$ and $SD_y$).

Given Data:

• The dataset includes: x &: 7, 9, 6, 4, 5, 3, 3, 7, 8 \\ y &: 19.9, 26.2, 18.8, 9.9, 14, 9.8, 7.3, 5.3, 14.5, 24 \end{aligned}$$

Step 1: Calculate the Mean ( $\bar{x}$ and $\bar{y}$ )

• $\bar{x} = \frac{\sum x_i}{n}$
• $\bar{y} = \frac{\sum y_i}{n}$

Step 2: Calculate the Standard Deviation ( $SD_x$ and $SD_y$ )

• Standard deviation formula: $SD = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}$

I will perform these calculations for you now.The calculations for the dataset are as follows:

1. Mean of $x$ ($\bar{x}$): 5.8 (rounded to one decimal place)
2. Mean of $y$ ($\bar{y}$): 14.0 (rounded to one decimal place)
3. Standard deviation of $x$ ($SD_x$): 2.2
4. Standard deviation of $y$ ($SD_y$): 6.7

Let me know if you'd like further details on these calculations or explanations!

Here are five questions that can expand on this concept:

1. How does the least squares regression line (LSRL) relate to the means of $x$ and $y$?
2. Can you calculate the correlation coefficient for this dataset?
3. How does the variability in $y$ (indicated by $SD_y$) compare to $x$'s variability?
4. How would you use the LSRL to predict a new $y$-value for a given $x$?
5. What effect does an outlier have on the LSRL and standard deviations?

Tip: Always double-check your values when computing standard deviations manually, especially when using large datasets!