Final answer:
The coefficient of correlation measures the strength and direction of the linear relationship between two variables. Using the given table of amusement park attendance, we can calculate the coefficient of correlation by finding the mean of the x and y values, calculating the deviations, and then applying the formula for correlation. The rounded coefficient of correlation is approximately 0.059.
Step-by-step explanation:
To find the coefficient of correlation, we need to use the given table of amusement park attendance. The coefficient of correlation, also known as the Pearson correlation coefficient, measures the strength and direction of the linear relationship between two variables.
Step 1: Calculate the mean of the x and y values.
Mean of x (years) = (2009 + 2010 + 2011 + 2012 + 2013) / 5 = 1110 / 5 = 222
Mean of y (attendance) = (107,348 + 109,321 + 112,509 + 116,420 + 119,951) / 5 = 565,549 / 5 = 113,110
Step 2: Calculate the deviation of each x and y value from their respective means.
x deviation = x value - mean of x
y deviation = y value - mean of y
Step 3: Calculate the product of the x and y deviations for each pair of values.
Step 4: Calculate the sum of the x deviations, y deviations, and the product of the x and y deviations.
Step 5: Calculate the correlation coefficient using the formula:
correlation = (sum of the x and y deviations) / sqrt((sum of the squared x deviations) * (sum of the squared y deviations))
Plugging in the values from the table:
x deviations: 2009 - 2009 = 0, 2010 - 2009 = 1, 2011 - 2009 = 2, 2012 - 2009 = 3, 2013 - 2009 = 4
y deviations: 107,348 - 113,110 = -5,762, 109,321 - 113,110 = -3,789, 112,509 - 113,110 = -601, 116,420 - 113,110 = 3,310, 119,951 - 113,110 = 6,841
Sum of the x deviations = 0 + 1 + 2 + 3 + 4 = 10
Sum of the y deviations = -5,762 + -3,789 + -601 + 3,310 + 6,841 = 656
Product of x and y deviations: 0*-5,762 + 1*-3,789 + 2*-601 + 3*3,310 + 4*6,841 = 8161
Sum of the squared x deviations: 0^2 + 1^2 + 2^2 + 3^2 + 4^2 = 30
Sum of the squared y deviations: (-5,762)^2 + (-3,789)^2 + (-601)^2 + 3,310^2 + 6,841^2 = 134,721,5
correlation = (10 * 656) / sqrt(30 * 134,721,521) = 6,560 / 111,751.539 = 0.058587
Rounding to the nearest thousandth, the coefficient of correlation is approximately 0.059.