To find the standard deviation of the data set \( {15, 18, 11, 17, 14} \), follow these steps:
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Calculate the Mean: \[ \text{Mean} = \frac{15 + 18 + 11 + 17 + 14}{5} = \frac{75}{5} = 15 \]
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Calculate the Differences from the Mean: \[ 15 - 15 = 0 \ 18 - 15 = 3 \ 11 - 15 = -4 \ 17 - 15 = 2 \ 14 - 15 = -1 \]
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Square the Differences: \[ 0^2 = 0 \ 3^2 = 9 \ (-4)^2 = 16 \ 2^2 = 4 \ (-1)^2 = 1 \]
Thus, the squared differences are: \[ 0, 9, 16, 4, 1 \]
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Calculate the Variance:
- Sum of Squared Differences: \[ 0 + 9 + 16 + 4 + 1 = 30 \]
- Variance (for population standard deviation): \[ \text{Variance} = \frac{\text{Sum of Squared Differences}}{n} = \frac{30}{5} = 6 \]
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Calculate the Standard Deviation: \[ \text{Standard Deviation} = \sqrt{6} \approx 2.44949 \]
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Round to the Nearest Hundredth: \[ 2.45 \]
The standard deviation of the dataset is \(\mathbf{2.45}\).
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