A traffic camera measured the speeds, x kilometres per hour, of 8 cars travelling along a certain street, with the following results.
62.7, 59.6, 64.2, 61.5, 68.3, 66.9, 62.0, 62.3
- Find \(\Sigma(x - 62)\).
- Find \(\Sigma(x - 62)^2\).
- Find the mean and variance of the speeds of the 8 cars.
Solution
(i) Calculate \(\Sigma(x - 62)\):
\((62.7 - 62) + (59.6 - 62) + (64.2 - 62) + (61.5 - 62) + (68.3 - 62) + (66.9 - 62) + (62.0 - 62) + (62.3 - 62) = 0.7 - 2.4 + 2.2 - 0.5 + 6.3 + 4.9 + 0 + 0.3 = 11.5\)
(ii) Calculate \(\Sigma(x - 62)^2\):
\((0.7)^2 + (-2.4)^2 + (2.2)^2 + (-0.5)^2 + (6.3)^2 + (4.9)^2 + (0)^2 + (0.3)^2 = 0.49 + 5.76 + 4.84 + 0.25 + 39.69 + 24.01 + 0 + 0.09 = 75.13\)
(iii) Calculate the mean and variance:
Mean \(= \frac{62.7 + 59.6 + 64.2 + 61.5 + 68.3 + 66.9 + 62.0 + 62.3}{8} = \frac{507.5}{8} = 63.4375\)
Variance \(= \frac{75.13}{8} - \left(\frac{11.5}{8}\right)^2 = 9.39125 - 2.06125 = 7.32\)
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