Question

Find the variance of -2,2,2,2?

Answer 1

To find the variance of the data set \(-2, 2, 2, 2\), we can follow these steps:

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

2. **Calculate the squared differences from the mean**:
- For \(-2\):
\[
(-2 - 1)^2 = (-3)^2 = 9
\]
- For \(2\):
\[
(2 - 1)^2 = (1)^2 = 1
\]
- For \(2\):
\[
(2 - 1)^2 = (1)^2 = 1
\]
- For \(2\):
\[
(2 - 1)^2 = (1)^2 = 1
\]

3. **Sum the squared differences**:
\[
9 + 1 + 1 + 1 = 12
\]

4. **Calculate the variance**:
- Since this is a sample, we divide by \(n-1\) (where \(n\) is the number of data points). Here, \(n = 4\).
\[
\text{Variance} = \frac{12}{4 - 1} = \frac{12}{3} = 4
\]

Therefore, the variance of the data set \(-2, 2, 2, 2\) is \(4\).