Question

Find the variance of -4,4,4,4?

Answer 1

To find the variance of the data set \(-4, 4, 4, 4\), we can follow these steps:

1. **Calculate the Mean**:
\[
\text{Mean} = \frac{(-4) + 4 + 4 + 4}{4} = \frac{8}{4} = 2
\]

2. **Calculate the Squared Differences from the Mean**:
- For \(-4\): \((-4 - 2)^2 = (-6)^2 = 36\)
- For \(4\): \((4 - 2)^2 = (2)^2 = 4\)
- For \(4\): \((4 - 2)^2 = (2)^2 = 4\)
- For \(4\): \((4 - 2)^2 = (2)^2 = 4\)

Now we have the squared differences: \(36, 4, 4, 4\).

3. **Calculate the Variance**:
The variance is the average of the squared differences.

First, find the sum of the squared differences:
\[
36 + 4 + 4 + 4 = 48
\]

Then divide by the number of data points (4):
\[
\text{Variance} = \frac{48}{4} = 12
\]

Thus, the variance of the data set \(-4, 4, 4, 4\) is \(\boxed{12}\).