To calculate the standard deviation of the given data (1, 1, 2, 3, 3), follow these steps:
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Calculate the mean (average) of the data: \[ \text{Mean} = \frac{\text{Sum of data}}{\text{Number of data points}} = \frac{1 + 1 + 2 + 3 + 3}{5} = \frac{10}{5} = 2 \]
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Calculate the deviations from the mean for each data point: \[ 1 - 2 = -1 \ 1 - 2 = -1 \ 2 - 2 = 0 \ 3 - 2 = 1 \ 3 - 2 = 1 \] So, the deviations are: -1, -1, 0, 1, 1.
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Square each of the deviations: \[ (-1)^2 = 1 \ (-1)^2 = 1 \ (0)^2 = 0 \ (1)^2 = 1 \ (1)^2 = 1 \] Thus, the squared deviations are: 1, 1, 0, 1, 1.
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Calculate the average of the squared deviations (this is the variance): \[ \text{Variance} = \frac{\text{Sum of squared deviations}}{\text{Number of data points}} = \frac{1 + 1 + 0 + 1 + 1}{5} = \frac{4}{5} = 0.8 \]
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Calculate the standard deviation by taking the square root of the variance: \[ \text{Standard Deviation} = \sqrt{0.8} \approx 0.8944 \]
Therefore, the standard deviation of the data is approximately 0.8944.