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 complete what is the variance? what is the standard deviation, rounded to the nearest whole number? done

Explanation:

Step1: Recall variance formula

The formula for the variance $s^{2}$ of a sample is $s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}$, where $\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}$ is the numerator and $n$ is the number of data - points. Here, we are given that the numerator $\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}=420000$ and $n = 6$.

Step2: Calculate variance

Using the formula $s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}$, substitute $\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}=420000$ and $n = 6$. Then $s^{2}=\frac{420000}{6 - 1}=\frac{420000}{5}=84000$.

Step3: Calculate standard deviation

The standard deviation $s$ is the square - root of the variance. So $s=\sqrt{s^{2}}=\sqrt{84000}\approx289.83\approx290$.

Answer:

Variance: $84000$
Standard deviation: $290$