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?

Explanation:

Calculate the population mean

Using the Population Mean Symbol knowledge point

$$ \mu = \frac{100 + 100 + 120 + 120 + 180}{5} = \frac{620}{5} = 124 $$

Calculate the squared deviations

Using the Population Variance Calculation knowledge point

$$
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$$

Calculate the population variance

Using the Population Variance Calculation knowledge point

$$ \sigma^2 = \frac{576 + 576 + 16 + 16 + 3136}{5} = \frac{4320}{5} = 864 $$

Calculate the population standard deviation

Using the Population Standard Deviation knowledge point

$$ \sigma = \sqrt{864} \approx 29.39 $$

Answer:

Question 1

The variance is <blank>864</blank>.

Question 2

The standard deviation is <blank>29.39</blank>.