The table below shows the height (in inches) and weight (in pounds) of eight basketball players.
Height=67 69 70 72 74 74 78 79
Weight=183 201 206 220 226 240 253 255
What is the correlation coefficient of the set of data? Round your answer to the nearest thousandth.
a. -0.946
b. 0.596
c. 0.035
d. 0.981***
Probably b.
Its D fa sho
To find the correlation coefficient of the set of data, we can use the Pearson correlation coefficient formula. The formula is as follows:
r = (Σ((xi - mean(x))(yi - mean(y)))) / sqrt(Σ((xi - mean(x))^2) * Σ((yi - mean(y))^2))
Where:
- r is the correlation coefficient
- xi and yi are the individual values of the two variables
- mean(x) and mean(y) are the means (averages) of the two variables
Using this formula, we can calculate the correlation coefficient step by step:
1. Calculate the means of the height and weight:
mean(height) = (67 + 69 + 70 + 72 + 74 + 74 + 78 + 79) / 8 = 72.375
mean(weight) = (183 + 201 + 206 + 220 + 226 + 240 + 253 + 255) / 8 = 228.5
2. Calculate the deviations from the means for both height and weight:
(height deviation) = (67 - 72.375), (69 - 72.375), (70 - 72.375), (72 - 72.375), (74 - 72.375), (74 - 72.375), (78 - 72.375), (79 - 72.375)
(weight deviation) = (183 - 228.5), (201 - 228.5), (206 - 228.5), (220 - 228.5), (226 - 228.5), (240 - 228.5), (253 - 228.5), (255 - 228.5)
3. Calculate the sum of the products of the deviations:
Σ((height deviation) * (weight deviation)) = (-5.375)(-45.5) + (-3.375)(-27.5) + (-2.375)(-22.5) + (-0.375)(-8.5) + (1.625)(-2.5) + (1.625)(11.5) + (5.625)(24.5) + (6.625)(26.5) = 600.875
4. Calculate the sum of the squares of the deviations for both height and weight:
Σ((height deviation)^2) = (-5.375)^2 + (-3.375)^2 + (-2.375)^2 + (-0.375)^2 + (1.625)^2 + (1.625)^2 + (5.625)^2 + (6.625)^2 = 118.375
Σ((weight deviation)^2) = (-45.5)^2 + (-27.5)^2 + (-22.5)^2 + (-8.5)^2 + (-2.5)^2 + (11.5)^2 + (24.5)^2 + (26.5)^2 = 6946.5
5. Calculate the square root of the product of the sums of the squares of the deviations:
sqrt(Σ((height deviation)^2) * Σ((weight deviation)^2)) = sqrt(118.375 * 6946.5) = sqrt(822736.125) ≈ 906.952
6. Finally, calculate the correlation coefficient using the formula:
r = (Σ((height deviation) * (weight deviation))) / sqrt(Σ((height deviation)^2) * Σ((weight deviation)^2))
= 600.875 / 906.952 ≈ 0.662 (rounded to three decimal places)
The correlation coefficient of the set of data is approximately 0.662. Therefore, the correct answer is NOT d. 0.981.