To find the variance for the given data, we can use the following formula:
Variance = (sum of squared deviations from the mean) / (number of data points)
First, we need to find the mean of the data:
mean = (-12 + 6 - 3 + 6) / 4 = -0.75
Next, we need to find the deviation of each data point from the mean:
deviations: (-12 - (-0.75)) = -11.25, (6 - (-0.75)) = 6.75, (-3 - (-0.75)) = -2.25, (6 - (-0.75)) = 6.75
Then, we square each deviation:
squared deviations: (-11.25)^2 = 126.5625, (6.75)^2 = 45.5625, (-2.25)^2 = 5.0625, (6.75)^2 = 45.5625
We add up these squared deviations:
sum of squared deviations = 222.75
Finally, we divide by the number of data points to get the variance:
variance = 222.75 / 4 = 55.6875
Rounding to one more decimal place than the original data, we get:
variance = 55.7