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1.9, 1.9, 2.7, 3.9, 4.9, 5.7, 7.3, 8.2 find the standard deviation

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Answer to a math question 1.9, 1.9, 2.7, 3.9, 4.9, 5.7, 7.3, 8.2 find the standard deviation

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Cristian
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111 Answers
1. Calculate the mean of the data:
\text{Mean} = \frac{1.9 + 1.9 + 2.7 + 3.9 + 4.9 + 5.7 + 7.3 + 8.2}{8} = \frac{36.5}{8} = 4.5625

2. Find the squared differences from the mean for each data point:
(1.9 - 4.5625)^2 = 6.8641
(1.9 - 4.5625)^2 = 6.8641
(2.7 - 4.5625)^2 = 3.4849
(3.9 - 4.5625)^2 = 0.4391
(4.9 - 4.5625)^2 = 0.1141
(5.7 - 4.5625)^2 = 1.2991
(7.3 - 4.5625)^2 = 7.4676
(8.2 - 4.5625)^2 = 13.2656

3. Calculate the variance:
\text{Variance} = \frac{6.8641 + 6.8641 + 3.4849 + 0.4391 + 0.1141 + 1.2991 + 7.4676 + 13.2656}{8} = \frac{39.7986}{8} = 4.9748

4. Finally, find the standard deviation:
\sigma = \sqrt{4.9748} \approx 2.23

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