To calculate the standard deviation of the prices of the decorations, follow these steps:
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Find the mean (average) of the data. \[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{1.00 + 3.00 + 2.00 + 6.00 + 9.00}{5} \] \[ \text{Mean} = \frac{21.00}{5} = 4.20 \]
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Calculate the deviations from the mean and square them. \[ (1.00 - 4.20)^2 = (-3.20)^2 = 10.24 \] \[ (3.00 - 4.20)^2 = (-1.20)^2 = 1.44 \] \[ (2.00 - 4.20)^2 = (-2.20)^2 = 4.84 \] \[ (6.00 - 4.20)^2 = (1.80)^2 = 3.24 \] \[ (9.00 - 4.20)^2 = (4.80)^2 = 23.04 \]
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Sum the squared deviations. \[ 10.24 + 1.44 + 4.84 + 3.24 + 23.04 = 43.80 \]
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Calculate the variance. The formula for the variance \( \sigma^2 \) when dealing with a sample is: \[ \text{Variance} = \frac{\text{Sum of squared deviations}}{n} \] where \( n \) is the number of data points. Here, \( n = 5 \). \[ \text{Variance} = \frac{43.80}{5} = 8.76 \]
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Calculate the standard deviation. \[ \sigma = \sqrt{\text{Variance}} = \sqrt{8.76} \approx 2.96 \]
Finally, round the result to the nearest ten cents: \[ \boxed{2.96} \]