Question

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

Answer 1

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. 

Answer 2

The variance of the five bedroom house is 864.

The formula variance

σ²

$=\frac{X^2}{N} -u^2$

To get the value of X²

= 100²+100²+120²+120²+180²

= 81200

The number is N = 5

u = mean

$u = \frac{100+100+120+120+180}{5}$

u = 124

The values in the variance formula

$\frac{81200}{5} -124^2$

16240-15376

= 864

The variance is 864

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