The scatter plot shows the relationship between the number of hours spent practicing piano per week and the number of pieces of music the student can play:
A scatter plot is shown. The x-axis is labeled hours spent practicing and the y-axis is labeled number of pieces student can play. Data points are located at 1 and 1, 1 and 5, 2 and 10, 2 and 15, 3 and 15, 3 and 25, 4 and 40, 5 and 40, 5 and 50, 6 and 55, 6 and 70, 8 and 90, 3 and 70. A circle labeled T includes all points except for 3 and 70. Point 3 and 70 is circled and labeled as R.
Part A: What is the group of points labeled T called? What is the point labeled R called? Give a possible reason for the presence of point R. (3 points)
Part B: Describe the association between the number of hours practiced each week and the number of pieces a piano student can play. (2 points)
Part A: The group of points labeled T is called a cluster, while the point labeled R is called an outlier. An outlier is a data point that differs significantly from other observations in a dataset. In this case, point R may represent a student who has an unusually high number of pieces they can play in relation to the number of hours they practice piano per week. This could be due to natural talent, previous experience, or other factors that are not accounted for in the data.
Part B: The association between the number of hours practiced each week and the number of pieces a piano student can play appears to be positive, as the more hours practiced, the higher the number of pieces the student can play. However, there is also variability in the data, as not all students who practice a certain number of hours per week have the same ability to play pieces. This variability is evident from the presence of the outlier point R.
Jordan plotted the graph below to show the relationship between the temperature of his city and the number of cups of hot chocolate he sold daily:
A scatter plot is shown with the title Jordans Hot Chocolate Sales. The x axis is labeled High Temperature and the y axis is labeled Cups of Hot Chocolate Sold. Data points are located at 20 and 20, 30 and 18, 40 and 20, 35 and 15, 50 and 20, 45 and 20, 60 and 14, 65 and 18, 80 and 10, 70 and 8, 40 and 2.
Part A: In your own words, describe the relationship between the temperature of the city and the number of cups of hot chocolate sold. (2 points)
Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate the slope and y-intercept. (3 points)
Part A: The relationship between the temperature of the city and the number of cups of hot chocolate sold appears to be negative, as the number of cups sold tends to decrease as the temperature increases.
Part B: To make the line of best fit, you would need to draw a line that represents the overall trend of the data points. The line should pass through the middle of the data points, minimizing the distance between the line and the points.
To calculate the slope of the line of best fit, we can choose two points and use the formula: slope = (y2 - y1) / (x2 - x1).
Let's choose the points (20, 20) and (80, 10).
slope = (10 - 20) / (80 - 20) = -10 / 60 = -1/6.
To find the y-intercept, we can use the formula: y = mx + b, where m is the slope and (x, y) is any point on the line.
Using point (20, 20):
20 = (-1/6)(20) + b
20 = -20/6 + b
b = 140/6 = 70/3 ≈ 23.3.
Therefore, the approximate equation of the line of best fit is: y = -1/6x + 70/3.
put it together in their separate A and B sentences pls
Part A: The relationship between the temperature of the city and the number of cups of hot chocolate sold is negative, as the number of cups sold tends to decrease as the temperature increases.
Part B: To create the line of best fit, the approximate slope of the line is -1/6 and the y-intercept is approximately 70/3 or 23.3.