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? what is the standard deviation?

Answer 1

Variance = 864

Standard Deviation= 29.4

Answer 2

Standard Deviation = 29.40

Variance = 864

Explanation:

A contractor records all of the bedroom areas, in square feet of a 5 bedroom house as : 100, 100, 120, 120, 180

To calculate the standard deviation first we have to calculate the mean of the data

( 100 + 100 + 120 + 120 + 180 ) / 5

= 620 / 5 = 124

Then for each number subtract the mean and square the result :

-24, -24, -4, -4, 56

square the result = 576, 576, 16, 16, 3136

Now work out the mean of these squared differences.

( 576 + 576 + 16 + 16 + 3136 ) / 5 = 4320 / 5 = 864

This value is Variance, so the variance = 864

Now we take the square root of 864 to get standard deviation

`√(864)` = 29.39 rounded to 29.40

Standard Deviation = 29.40

Variance = 864