To calculate the standard deviation, we need to follow these steps:
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Calculate the Mean (Average): \[ \text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}} = \frac{15 + 18 + 11 + 17 + 14}{5} = \frac{75}{5} = 15 \]
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Calculate the Differences from the Mean:
- \(15 - 15 = 0\)
- \(18 - 15 = 3\)
- \(11 - 15 = -4\)
- \(17 - 15 = 2\)
- \(14 - 15 = -1\)
The differences from the mean are: \(0, 3, -4, 2, -1\).
- Square the Differences:
- \(0^2 = 0\)
- \(3^2 = 9\)
- \((-4)^2 = 16\)
- \(2^2 = 4\)
- \((-1)^2 = 1\)
The squared differences are: \(0, 9, 16, 4, 1\).
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Calculate the Variance: Sum the squared differences: \[ 0 + 9 + 16 + 4 + 1 = 30 \] Divide by the number of data points: \[ \text{Variance} = \frac{30}{5} = 6 \]
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Calculate the Standard Deviation: Take the square root of the variance: \[ \text{Standard Deviation} = \sqrt{6} \approx 2.45 \]
The standard deviation of the data set, rounded to the nearest hundredth, is approximately 2.45.