Question

calculate standa a contractor records the areas, in square feet, of a small sample of houses in a neighborhood to determine data about the neighborhood. the areas 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? \\( (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 \\) retry

Explanation:

Step1: Calculate sample mean

First, list the data: $2400, 1750, 1900, 2500, 2250, 2100$.
Sum the data: $2400 + 1750 + 1900 + 2500 + 2250 + 2100 = 12900$
Mean $\bar{x} = \frac{12900}{6} = 2150$

Step2: Find each data - mean difference

Calculate $(x_i - \bar{x})$ for each value:
$2400 - 2150 = 250$
$1750 - 2150 = -400$
$1900 - 2150 = -250$
$2500 - 2150 = 350$
$2250 - 2150 = 100$
$2100 - 2150 = -50$

Step3: Square and sum differences

Square each difference and sum them:
$(250)^2 + (-400)^2 + (-250)^2 + (350)^2 + (100)^2 + (-50)^2$
$=62500 + 160000 + 62500 + 122500 + 10000 + 2500 = 420000$

Answer:

$\boldsymbol{(250)^2 + (-400)^2 + (-250)^2 + (350)^2 + (100)^2 + (-50)^2 = 420,000}$