Question

Find the variance of -6,6,6,6?

Answer 1

To find the variance of the data set \(-6, 6, 6, 6\), you can follow these steps:

1. **Calculate the mean**:

\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{-6 + 6 + 6 + 6}{4} = \frac{12}{4} = 3
\]

2. **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 \(6\): \((6 - 3)^2 = (3)^2 = 9\)

3. **Sum the squared deviations**:

\[
81 + 9 + 9 + 9 = 108
\]

4. **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 \(27\).