To calculate the standard deviation, we need to follow these steps:
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List the data points: Based on the table, we can create the data points based on the "Number of Days":
- For -1 minutes: 1 day
- For 0 minutes: 2 days
- For 1 minute: 4 days
- For 2 minutes: 2 days
- For 3 minutes: 1 day
Thus, the data set is: \(-1, 0, 0, 1, 1, 1, 1, 2, 2, 3\).
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Calculate the mean: \[ \text{Mean} (\mu) = \frac{\text{Sum of all data points}}{\text{Total number of data points}} \] \[ \text{Mean} = \frac{(-1) + (0 \cdot 2) + (1 \cdot 4) + (2 \cdot 2) + (3)}{10} = \frac{-1 + 0 + 4 + 4 + 3}{10} = \frac{10}{10} = 1 \]
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Calculate the variance: \[ \text{Variance} = \frac{\sum (x_i - \mu)^2}{N} \] where \(x_i\) are the data points and \(N\) is the total number of data points.
Calculate each variance component:
- For \(-1\): \((-1 - 1)^2 = (-2)^2 = 4\)
- For \(0\): \((0 - 1)^2 = (-1)^2 = 1\) (2 days, so multiply by 2)
- For \(1\): \((1 - 1)^2 = (0)^2 = 0\) (4 days, so multiply by 4)
- For \(2\): \((2 - 1)^2 = (1)^2 = 1\) (2 days, so multiply by 2)
- For \(3\): \((3 - 1)^2 = (2)^2 = 4\)
Now calculate the total variance: \[ \text{Total Sum} = 4 + (1 \cdot 2) + (0 \cdot 4) + (1 \cdot 2) + 4 = 4 + 2 + 0 + 2 + 4 = 12 \] \[ \text{Variance} = \frac{12}{10} = 1.2 \]
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Calculate the standard deviation: \[ \text{Standard Deviation} (\sigma) = \sqrt{\text{Variance}} = \sqrt{1.2} \approx 1.095 \]
Rounding to the nearest tenth: The standard deviation is approximately 1.1.
So your original answer is confirmed: the standard deviation is 1.1.