Question

a contractor records the areas, in square feet, of a small sample of houses in a neighborhood to determine data about the neighborhood. they are: 2,400; 1,750; 1,900; 2,500; 2,250; 2,100 which of the following represents the numerator in the calculation of variance and... (225)² + (-425)² + (-275)² + (325)² + (75)² +... = 42...750 (650)² + (-150)² + (-600)² + (250)² + (150)² + (-300)² = 980,000 (250)² + (-400)² + (-250)² + (350)² + (100)² + (-100)² = 420,000 what is the variance? what is the standard deviation, rounded to the nearest whole number?

Explanation:

Step1: Calculate the sample mean

First, sum all the values and divide by the count of values.
$$\text{Mean} = \frac{2400 + 1750 + 1900 + 2500 + 2250 + 2100}{6} = \frac{12900}{6} = 2150$$

Step2: Confirm the numerator (sum of squared deviations)

From the correct option, the sum of squared deviations is $420000$.

Step3: Calculate sample variance

Divide the numerator by $n-1$ (sample variance formula).
$$\text{Variance} = \frac{420000}{6-1} = \frac{420000}{5} = 84000$$

Step4: Calculate standard deviation

Take the square root of the variance, then round.
$$\text{Standard Deviation} = \sqrt{84000} \approx 289.83 \approx 290$$

Answer:

Variance: $84000$
Standard Deviation: $290$