Wiki Page, Math 13 - Perez Sandbox : Exam 1 Review

Wiki Page
2026-01-17T21:15:00-08:00

General/Misc

1. Are we going to have a lab portion on the test where we must use Desmos to make graphs?

No. The exam will be only written responses, some of which will be your analysis and interpretation of graphs that are provided to you.

2. How can we use StatCrunch? It asks me for a code.

You don't need to use StatCrunch for anything. I used Statcrunch in previous semesters but I'm not using it anymore.

Instead of Statcrunch, you can use Desmos or the Art of Stat web apps. However, you won't need to make any graphs for the exam.

Please let me know the exact page or assignment where you see references to Statcrunch so I can remove them.

3. I am still having trouble understanding the difference between categorical and quantitative variables. What is a good way to differentiate between the two?

The way I differentiate them is this: You can take the average of quantitative variables, but you can't for categorical variables.

For example, if Milena is 5 feet tall and Davit is 6 feet tall:

We can take the average of their heights, so Height is a quantitative variable.

We can't take the average of their names, so Name is a categorical variable.

4. Are there certain equations that we should have memorized before the exam?

No. The exam is open-notes and open-book.

5. I get very confused when prompted "Compare characteristics of the two distributions, instead of just listing observations about the distributions." What would be the technique behind it? I'm pretty sure that listing what are similar and what are different is not enough.

In most cases, listing what are similar and different is enough, as long as the characteristics you're comparing are things that we've studied in class, like shape, spread, center, etc.

6. I still do not understand how to save in Canvas.

A short version to save and embed a picture in Canvas:

Click "Insert," then choose "Image" and then "Upload Image."

Choose the image you have saved on your computer that you want to upload.

Click "Submit" and you're done!

7. Are we going to get more videos that can help us with the exam?

Just this one! Actually, there will be a HW session on Wednesday at 2pm where you can ask more questions if you want.

Unit 2 (Dot plots, Histograms, Boxplots, Standard Deviation)

8. When to use the histogram or boxplot? I'm a little confused still on how to tell which is the best type of graph for the data we receive.

If you're not sure which one to use, I recommend making both graphs and choosing whichever your think is more clear.

It's pretty easy in Desmos to make both of them in the same graph if you want to do so, like this:

9. Can you review 5 number summary and IQR and how to estimate when looking at boxplots and bar charts?

If you look at the boxplot in the picture above, you should be able to determine the 5-number summary.

The box goes from Q1 to Q3. It looks like Q1 is 0 and Q3 is 7, because that's where the boundary lines for the box are, on the x-axis.

The median (or Q2) is where the line inside the box is, on the x-axis. It looks like Q2 is at 1

The minimum is the lowest (or left-most) point on the boxplot. Here, it looks like the minimum is 0.

The maximum is the highest (or right-most) point on the boxplot. Here, it looks like the maximum is 36.

Therefore, the 5-number summary is 0,0,1,7,36.

If you have the data in Desmos, you can get the 5-number summary by typing "stats(D)" (if your list is called D), like this:

10. Can you review info about outliers and when they can be discarded vs when they are required to be included.

It's good practice to include outliers unless you have some good reason not to do so. If you're not sure if you have a good reason, then you don't have one!

11. One question that I had was what is the difference between ADM in the median and in the mean? In which situation would we use either or?

We only use ADM with the mean. ADM stands for Average Difference from the Mean.

12. What is the difference between ADM and standard deviation?

The ADM and the standard deviation are very similar. They both measure slightly different averages of the the distances to the mean.

The ADM is easier to understand and calculate by hand. The standard deviation is easier to do calculus on (although we won't be doing that!).

We only talked about ADM to introduce the concept of standard deviation, which we will be using for the rest of the semester.

13. How to create the histogram, boxplot, and scatter chart in Excel.

You won't have to do this for the exam, but I'd be happy to make a separate video on how to do this upon request.

Unit 3 (Scatterplots, Linear Regression)

14. What is the difference between using dot plot and Scatterplot?

A dotplot is a graph of one quantitative variable. There is only one horizontal number line.

A scatterplot is the graph of two variables at the same time. There are two number lines, one horizontal and one vertical.

15. How can we really know the correct numbers on a scatter plot?

If you need to know the exact x- and y-coordinates of points in a scatterplot, you will have to have access to the data that was used to make the graph.

If you are interacting with a scatterplot in Desmos or some other graphing software, you can usually get the coordinates of a point by clicking on the point, like this:

16. What does it mean when the dots on a scatter plot are shaped like a circle?

It doesn't mean anything. For example, in Desmos, you can choose to make the points be dots, circles or x's.

17. What does it mean when there’s more than one outlier on a scatter plot?

It doesn't mean anything in particular.

18. Also wanted clarification on these answers and difference between explanatory, response or neither.

We are told that faculty "plan to use the number of workshops attended to predict the final exam score." This means that the number of workshops attended is the explanatory variable and the final exam score is the response variable.

Every other variable is not the explanatory or the response variable for this study (even though they could be used as the explanatory or response variable in some other study).

19. Another question I was not quite understanding.

The y-intercept of the regression line is the predicted y-value if the x-value is equal to 0. It is the number in the equation that isn't multiplied by the x-value.

For the equation in the problem, if the x-value (or pre-statistics course grade) is 0, then the predicted y-value (or introductory statistics course grade) is -0.147.

Note that this prediction doesn't make sense! This is because the x-value of 0 is far outside of the points in our scatterplot. This is an extrapolation, which often doesn't have much predictive value.

20. One of my questions is how the least squares regression line is found and how the answer came out to be greater than 20.

There is a complicated formula for the linear regression line that we don't need to know, because we use software to calculate it. You can look it up if you want!

The linear regression line is the one that minimizes the SSE (sum of squared errors), so any other line will have a larger SSE.

The lengths of the green vertical lines in the picture are the errors. The SSE is the what you get you square each of those lengths and add them together.

21. I had another question about what the value of the standard error of regression tells us. I was not sure how to solve this.

is the the standard deviation of the prediction errors. In the example in #20 about, the prediction errors are the lengths of the green lines in the graph.

The standard deviation of the differences is close to the average difference.

From Module 9:

Standard error of the regression: Standard error is the standard deviation of the prediction errors.
is roughly a measure of the average amount that the predicted Y-values deviate from the observed Y-values, which is an estimate of the average distance that the data points are from the line. In other words, is roughly the average amount of prediction error for the regression line.

22. Linear Regression- Will the formulas be given to me?

No, but you won't need them.

23. Each line has a different formula?

Every line has an equation. Different lines have different equations.

For example, these equations will have different lines as their graphs: y=2+3x and y=3+2x.

24. Is there a formula to tell if something is an extrapolation? Just like there is the outlier formula?

That's an excellent question!

If there is a formula for it, I don't know it. For the purposes of our class, we will determine that it is an extrapolation if the x-value is outside the interval between the min and max of all the x-values.

25. In the scatterplots how will we know exactly the correlation? is there an equation or will this just be better with practice?

There is a precise formula for r, but you don't need to know it. We will use calculator programs to find r for us.

26. Are there any tips about how to estimate the correlation coefficient when looking at scatterplots? Visual estimations are tough for me.

You don't need to be good at estimating r, beyond being able to tell whether r is negative or positive.

27. You mentioned the confusion between y=mx+b and the current equation y=a+bx. Is this (y=a+bx) the equation we will use moving forward?

In this class, we will use y=a+bx, which is pretty standard in statistics.

We all learned y=mx+b in algebra class, which is an equivalent equation, but it uses b for the y-intercept instead of the slope. It's confusing because we use the letter b for two different things! I'd prefer there was better standardization, but no one asked me.

28. One of the things I need help understanding is SSE, more along the lines of interpreting it in my own words. Could you use more clarification on the term?

SSE stat

29. I would like a little more help on correlations coefficient, on how to find, just need a little more help on this.

If you need to find r, you should use a calculator or statistics software.

Here's a video showing how to find r using Desmos: How to use Desmos to make scatterplots and calculate correlation coefficients

30. I would like to review r and what different graphs look like based on r.

The correlation coefficient r is a measure of how linear the data is. A value of -1 or 1 means the data is perfectly linear.

The value of r is always between -1 and 1. The less linear the data is, the closer r is to 0.

Here is a graph I made in Desmos where you can see what different values of r look like.

31. Do curved shapes of charts always have certain values of r that they stay between?

Great question! Yes they do, although we usually just use in those situations, not r.

Here's an example from Desmos:

32. Why does outlier change the R? If we have a positive slope and the outlier is in the line does it still change the R or no, why?

In a scatterplot, we consider a point an outlier if it breaks the pattern that we see in the other points. So, we wouldn't consider a point on the regression line to be an outlier.

Here are three examples of different r-values depending on the where the extra black point is placed:

In the graph above, r=1.

In the graph above, r=0.7253.

In the graph above, r=0.2417.