Acontractor records all of the bedroom areas, in square feet, of a five-bedroom house as: 100, 100, 120, 120, 180 what is the variance?

The variance is the total of the squared distances of the given data from the mean. 

This can be calculated through the equation,
        
                            σ² = summation of X² / N  - μ²

where σ² is the variance X's are the data, N is the number of terms, and μ is the mean.

   summation of X² = 100² + 100² + 120² + 120² + 180² = 81200
                          N = 5
                                        μ = (100 + 100 + 120 + 120 + 180) / 5
                                         μ = 124

Substituting these values to the equation for variance,
                                 
                              σ² = (81200/5) - 124² = 864

Thus, the variance is equal to 864.