a contractor records the areas, in square feet, of a small sample of houses in a neighborhood to determine…

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 done

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 done

Answer

Answer:

First, we need to find the mean of the data - set. The data - set is (x = {2400,1750,1900,2500,2250,2100}). The number of data points (n = 6). The mean (\bar{x}=\frac{2400 + 1750+1900 + 2500+2250+2100}{6}=\frac{12900}{6}=2150).

Next, we find the deviation of each data point from the mean ((x_i-\bar{x})) and then square it ((x_i - \bar{x})^2). For (x_1 = 2400): (x_1-\bar{x}=2400 - 2150=250), ((x_1-\bar{x})^2=(250)^2) For (x_2 = 1750): (x_2-\bar{x}=1750 - 2150=-400), ((x_2-\bar{x})^2=(-400)^2) For (x_3 = 1900): (x_3-\bar{x}=1900 - 2150=-250), ((x_3-\bar{x})^2=(-250)^2) For (x_4 = 2500): (x_4-\bar{x}=2500 - 2150=350), ((x_4-\bar{x})^2=(350)^2) For (x_5 = 2250): (x_5-\bar{x}=2250 - 2150=100), ((x_5-\bar{x})^2=(100)^2) For (x_6 = 2100): (x_6-\bar{x}=2100 - 2150=-50), ((x_6-\bar{x})^2=(-50)^2)

The sum of the squared - deviations (\sum_{i = 1}^{n}(x_i-\bar{x})^2=(250)^2+(-400)^2+(-250)^2+(350)^2+(100)^2+(-50)^2=62500 + 160000+62500 + 122500+10000 + 2500=420000)

So the numerator in the calculation of variance and standard deviation is ((250)^2+(-400)^2+(-250)^2+(350)^2+(100)^2+(-50)^2 = 420000)

The correct option is ((250)^2+(-400)^2+(-250)^2+(350)^2+(100)^2+(-50)^2 = 420000)

Explanation:

Step1: Calculate the mean

(\bar{x}=\frac{2400 + 1750+1900 + 2500+2250+2100}{6}=2150)

Step2: Calculate the squared - deviations

((2400 - 2150)^2=(250)^2), ((1750 - 2150)^2=(-400)^2), ((1900 - 2150)^2=(-250)^2), ((2500 - 2150)^2=(350)^2), ((2250 - 2150)^2=(100)^2), ((2100 - 2150)^2=(-50)^2)

Step3: Sum the squared - deviations

(\sum=(250)^2+(-400)^2+(-250)^2+(350)^2+(100)^2+(-50)^2=420000)