Scatterplots to visually describe data that does not fit the definition of a function, but when you still want to compare one category of data to another category (independent vs dependent in science…. Y versus X in math….. output based on a varying input in both)

Project expectations… Ultimately, you need to create and determine a LINE of BEST FIT, for the data that you and your class chooses. This will be in the linear model of a y=mx+b equation.

We are using worldometer.org to get data on 30 countries. Specifically, the total number of deaths in the country from Covid-19 (rounded to the nearest hundred), compared to the population of the country (rounded to the nearest TENTH of a million).

About 20 countries were already picked and their data shared via your classroom chat feature on Monday of this week. You need to pick addition countries to get your list up to 30 countries.

PRESENT a clear table of the data. 3 columns. Country name, deaths, population.

PRESENT a clear scatterplot graph of the data, with scale ranges that best show all 30 points.

If you use DESMOS to help you, take a clear photo/screenshot. Or create your scatterplot on paper after looking at DESMOS as a guide.

TAKE your time, to draw a LINE of BEST FIT, ON your graph. The line should follow our discussions in class about being close to as many points as possible, while looking at patterns of where and how far away the line is from those points not near the best fit line.

(Be creative if needed, if you are using a screen shot photo, you could even tape string or a shoelace across the scatterplot)

Now the math part… find two places on your best fit line where you can confidently determine the population and deaths (the x and y value) possibly by estimating near major grid lines of your scale. These two places will become point 1 and point 2. Point 1 (x1,y1) and point 2 (x2,y2). Using these two points which might be real countries or estimated points, determine the slope of your best fit line (using the m=y2 minus y1 over x2 minus x1). After determining the slope, the determine the beginning point of your line using ALGEBRA, so that you can ultimately determine the EQUATION (y=mx+b) of your BEST FIT LINE to your scatterplot data.

Answer 3-5 questions, and include your answers in your project submission. Example… what would your best fit line equation predict to be the number of deaths for a country with 120 million people? How does Japan’s numbers compare to your best fit line predictions? Which 2 countries best show why this data does not represent a function? ….

1. USING your y=mx+b best fit line equation, what would your equation show as a reasonable estimate for the number of total deaths, for a country with 100 million people?

SHOW your work, just a couple steps of algebra would be appropriate.

2. USING your y=mx+b best fit line equation, what would your equation show would be a estimate for a country like the USA, with a population of 330 million people… How many people in that country would have died if it was exactly following your y=mx+b equation…. ?

3. Of the 4 made up countries I am about to list… please explain which 2 countries best show that our data, can not be a function. Explain with one or two sentences, …

Name	Population (x variable)	Total Deaths (y variable)
Applewoodstan	30	19,000
SteepSteepistan	50	25.000
Crowdedistan	50	45,000
Wildestolia	70	45,000

4. Look at your real worldometer data point for JAPAN, and try to discuss where that data point is compared to where your best fit line would estimate for a country of Japan’s population. If you don’t have Japan selected as a point, add it to your graph. In a few sentences, why do you think the data for Japan is so far from your best fit line? Remember, our data is not a function, because of other factors besides population that probably influenced why a country had a high or low total death count.