# 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?

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## Answers

Variance = 864Standard Deviation= 29.4

Answer:Standard Deviation = 29.40Variance = 864Step-by-step explanation:A contractor records all of the bedroom areas, in square feet of a 5 bedroom house as : 100, 100, 120, 120, 180To calculate the standard deviation first we have to calculate the mean of the data ( 100 + 100 + 120 + 120 + 180 ) / 5 = 620 / 5 = 124Then 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 = 864This value is Variance, so the variance = 864Now we take the square root of 864 to get standard deviation[tex]\sqrt{864}[/tex] = 29.39 rounded to 29.40Standard Deviation = 29.40Variance = 864