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Answer :
Final answer:
The standard deviation of the smokers group is approximately 16.57 and the standard deviation of the nonsmokers group is approximately 6.89.
Explanation:
To calculate the standard deviation for both groups, we need to follow the steps mentioned earlier:
- Calculate the mean of the data set for each group.
- Subtract the mean from each data value and square the result.
- Calculate the mean of the squared differences for each group.
- Take the square root of the mean of the squared differences for each group.
Let's calculate the standard deviation for both groups:
Smokers:
Mean = (69.3 + 56.0 + 22.1 + 47.6 + 53.2 + 48.1 + 52.7 + 34.4 + 60.2 + 43.8 + 23.2 + 13.8 + 28.4) / 13 = 43.6
Subtract the mean from each data value and square the result:
(69.3 - 43.6)^2 = 669.64
(56.0 - 43.6)^2 = 154.24
(22.1 - 43.6)^2 = 459.21
(47.6 - 43.6)^2 = 16.00
(53.2 - 43.6)^2 = 92.16
(48.1 - 43.6)^2 = 20.25
(52.7 - 43.6)^2 = 82.81
(34.4 - 43.6)^2 = 84.64
(60.2 - 43.6)^2 = 275.84
(43.8 - 43.6)^2 = 0.04
(23.2 - 43.6)^2 = 420.64
(13.8 - 43.6)^2 = 912.04
(28.4 - 43.6)^2 = 230.40
Calculate the mean of the squared differences:
(669.64 + 154.24 + 459.21 + 16.00 + 92.16 + 20.25 + 82.81 + 84.64 + 275.84 + 0.04 + 420.64 + 912.04 + 230.40) / 13 = 274.42
Take the square root of the mean of the squared differences:
sqrt(274.42) ≈ 16.57
Nonsmokers:
Mean = (28.6 + 25.1 + 26.4 + 34.9 + 29.8 + 31.8 + 41.6 + 21.1 + 36.0 + 37.9 + 13.9 + 38.5 + 30.2 + 30.6) / 14 = 30.79
Subtract the mean from each data value and square the result:
(28.6 - 30.79)^2 = 4.79
(25.1 - 30.79)^2 = 32.49
(26.4 - 30.79)^2 = 18.09
(34.9 - 30.79)^2 = 17.16
(29.8 - 30.79)^2 = 0.98
(31.8 - 30.79)^2 = 1.04
(41.6 - 30.79)^2 = 116.64
(21.1 - 30.79)^2 = 93.21
(36.0 - 30.79)^2 = 27.04
(37.9 - 30.79)^2 = 50.41
(13.9 - 30.79)^2 = 287.04
(38.5 - 30.79)^2 = 59.84
(30.2 - 30.79)^2 = 0.35
(30.6 - 30.79)^2 = 0.03
Calculate the mean of the squared differences:
(4.79 + 32.49 + 18.09 + 17.16 + 0.98 + 1.04 + 116.64 + 93.21 + 27.04 + 50.41 + 287.04 + 59.84 + 0.35 + 0.03) / 14 = 47.47
Take the square root of the mean of the squared differences:
sqrt(47.47) ≈ 6.89
Therefore, the standard deviation of the smokers group is approximately 16.57 and the standard deviation of the nonsmokers group is approximately 6.89.
Learn more about standard deviation here:
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