To calculate the variance for the data set \(10, 19, 21, 28, 12, 20, 16\), follow these steps:
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Calculate the mean:
\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{10 + 19 + 21 + 28 + 12 + 20 + 16}{7} = \frac{126}{7} = 18 \]
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Calculate the squared differences from the mean:
\[ (10 - 18)^2 = (-8)^2 = 64 \] \[ (19 - 18)^2 = (1)^2 = 1 \] \[ (21 - 18)^2 = (3)^2 = 9 \] \[ (28 - 18)^2 = (10)^2 = 100 \] \[ (12 - 18)^2 = (-6)^2 = 36 \] \[ (20 - 18)^2 = (2)^2 = 4 \] \[ (16 - 18)^2 = (-2)^2 = 4 \]
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Sum the squared differences:
\[ 64 + 1 + 9 + 100 + 36 + 4 + 4 = 218 \]
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Calculate the variance: Since this is a sample, we use \(n - 1\) (where \(n\) is the number of data points) for the denominator:
\[ \text{Variance} = \frac{\text{Sum of squared differences}}{n - 1} = \frac{218}{7 - 1} = \frac{218}{6} \approx 36.3333 \]
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Round to the nearest hundred:
Since \(36.3333\) rounded to the nearest hundred is \(0\).
Thus, the variance of the data set rounded to the nearest hundred is 0.