To find the variance of the data set \(-6, 6, 6, 6\), you can follow these steps:
- Calculate the mean:
\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{-6 + 6 + 6 + 6}{4} = \frac{12}{4} = 3 \]
- Calculate each value's deviation from the mean and square it:
- For \(-6\): \((-6 - 3)^2 = (-9)^2 = 81\)
- For \(6\): \((6 - 3)^2 = (3)^2 = 9\)
- For \(6\): \((6 - 3)^2 = (3)^2 = 9\)
- For \(6\): \((6 - 3)^2 = (3)^2 = 9\)
- Sum the squared deviations:
\[ 81 + 9 + 9 + 9 = 108 \]
- Divide by the number of values (since this is a population variance):
\[ \text{Variance} = \frac{108}{4} = 27 \]
Thus, the variance of the data set \(-6, 6, 6, 6\) is \(27\).