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 standard deviation?

(225)^2 + (-425)^2 + (-275)^2 + (325)^2 + (75)^2 + (-75)^2 = 423,750
(650)^2 + (-150)^2 + (-600)^2 + (250)^2 + (150)^2 + (-300)^2 = 980,000
(250)^2 + (-400)^2 + (-250)^2 + (350)^2 + (100)^2 + (-50)^2 = 420,000

Explanation:

Calculate the sample mean

Using the Sample Variance Formula and Sample Standard Deviation Formula knowledge points

$$
LATEXBLOCK0
$$

Compute the deviations from the mean

Using the Sample Variance Formula knowledge point

$$
LATEXBLOCK1
$$

Formulate the sum of squared deviations

Using the Sample Variance Formula knowledge point

$$
LATEXBLOCK2
$$

Answer:

• (A) \((225)^2 + (-425)^2 + (-275)^2 + (325)^2 + (75)^2 + (-75)^2 = 423,750\)
• (B) \((650)^2 + (-150)^2 + (-600)^2 + (250)^2 + (150)^2 + (-300)^2 = 980,000\)
• (C) \((250)^2 + (-400)^2 + (-250)^2 + (350)^2 + (100)^2 + (-50)^2 = 420,000\) (Correct answer)