To find the correlation coefficient, r, we first need to calculate the mean of the dosage (x) and rise in blood sugar level (y):
Mean of x:
(45 + 68 + 70 + 76 + 87) / 5 = 69.2
Mean of y:
(27 + 19 + 18 + 24 + 17) / 5 = 21
Next, we calculate the numerator of the formula for the correlation coefficient:
Σ((x - mean of x)(y - mean of y)):
(45 - 69.2)(27 - 21) + (68 - 69.2)(19 - 21) + (70 - 69.2)(18 - 21) + (76 - 69.2)(24 - 21) + (87 - 69.2)(17 - 21)
= (-24)(6) + (-1.2)(-2) + (0.8)(-3) + (6.8)(3) + (17.8)(-4)
= -144 + 2.4 - 2.4 + 20.4 - 71.2
= -194.8
Now, we calculate the denominator of the formula for the correlation coefficient:
√(Σ(x - mean of x)^2 * Σ(y - mean of y)^2):
√((-24)² + (-1.2)² + (0.8)² + (6.8)² + (17.8)²) * (√(6² + (-2)² + (-3)² + 3² + (-4)²)
= √(576 + 1.44 + 0.64 + 46.24 + 316.84) * √(36 + 4 + 9 + 9 + 16)
= √(940.16) * √(74)
= 30.668 * 8.602
= 263.693
Finally, we calculate the correlation coefficient, r:
r = -194.8 / 263.693
r ≈ -0.738
Therefore, the correlation coefficient for the given data is approximately -0.738.