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 \(4\).