Therefore it is clear which result is correct. Two alternatives are silly because they show a negative slope, but our data is definitely increasing. Because we are using a line of best fit and the scale of the vertical axis is large, this answer is a little off of the alternatives we are given. So the slope of the line is 10/8 percent per year which is 5/4 % per year or about 1.25% per year. To calculate the slope, (55-45)% is the amount the vertical height changed and the length of time in years was 9 - 1 = 8 years. The y- coordinates were 45 and 55 and those are in percent, remember. Sal chose to look at the percentage at 1 year and at 9 years. It is best not to choose two points that are really close together, and your result will be most accurate if you find a point that is exactly at the crossing of two grid marks AND on the line of best fit. To find our the rate of change, we calculate the slope of the line that is closest to all the points, running at about the same slope as the group of points. That is a rate of change problem, so we need to find the amount the vertical height of the data points is changing for every increase in the horizontal axis. Instead, we need to find the average yearly change in percentage. Add categorical variables to scatterplots. So this is not about calculating percentage based on numbers of people. Based on Chapter 4 of The Basic Practice of Statistics (6th ed.) Concepts: Displaying Relationships: Scatterplots Interpreting Scatterplots Adding Categorical Variables to Scatterplots Measuring Linear Association: Correlation Facts About Correlation Objectives: Construct and interpret scatterplots. adults that have this opinion), while the horizontal axis is in years, so percents are already there in the problem. In this case, the vertical axis is already in percents (Percentage of U.S. In other words, we use the slope of an imaginary line that passes through the points to help us choose good points for calculating the answer. 33% -7% 0% 1% are all correctly calculated from the data points, but they are wildly different and none of them is a good answer. The calculation is (50 - 42)/(9 - 0) which is 8/8 or 1% per yearĤ%. If we choose 0 years and 9 years, the percentages are 42 and 50 The calculation is (48 - 48)/(5 - 2) which is 0/3 or 0% per year (no change) If we choose 2 years and 5 years, the percentages are 48 and 48 If we choose 3 years and 4 years, the percentages are 54 and 47 The calculation is (47 - 46)/(4 - 1) which is 1/3 or 0.33% per year If we choose 1 year and 4 years, the percentages are 46 and 47 The calculation is (46 - 42)/(1 - 0) which is 4/1 or 4% per year If we choose 0 years and 1 year, the percentages are 42 and 46 Here are some of the coordinates from that graph that we can use: If we don't have a line of best fit, how do we find the rate of change? Well, that would be how much the data increases between points, divided by the measurement increase along the x-axis, which in this case is years.īut then we have to choose points to use to find the rate of change. Lucky for us, in this case, WE didn't have to draw the line of best fit-it was given to us.
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