a student fitted the line l to the data points (0,3), (2,3.6) (3,6), 6,3) find the center of gravity
To find the center of gravity for the given data points, you need to calculate the average of the x-coordinates and the average of the y-coordinates. The center of gravity, also known as the centroid, is the point (x_avg, y_avg) where x_avg is the average of the x-coordinates and y_avg is the average of the y-coordinates.
Let's calculate it step by step:
Step 1: Calculate the sum of the x-coordinates.
0 + 2 + 3 + 6 = 11
Step 2: Calculate the sum of the y-coordinates.
3 + 3.6 + 6 + 3 = 15.6
Step 3: Calculate the total number of data points, which is 4 in this case.
Step 4: Calculate the average of the x-coordinates.
x_avg = sum of x-coordinates / number of data points
x_avg = 11 / 4
x_avg = 2.75
Step 5: Calculate the average of the y-coordinates.
y_avg = sum of y-coordinates / number of data points
y_avg = 15.6 / 4
y_avg = 3.9
Therefore, the center of gravity is located at (2.75, 3.9).