Answered

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:

[tex]2400, 1750, 1900, 2500, 2250, 2100[/tex]

Which of the following represents the numerator in the calculation of variance and standard deviation?

A. [tex](225)^2 + (-425)^2 + (-275)^2 + (325)^2 + (75)^2 + (-75)^2 = 423,750[/tex]

B. [tex](650)^2 + (-150)^2 + (-600)^2 + (250)^2 + (150)^2 + (-300)^2 = 980,000[/tex]

C. [tex](250)^2 + (-400)^2 + (-250)^2 + (350)^2 + (100)^2 + (-50)^2 = 420,000[/tex]



Answer :

GinnyAnswer
To determine the numerator in the calculation of variance and standard deviation, we must follow these steps:

1. Find the Mean of the Sample:

The areas of the houses in the sample are:
[tex]\[ 2400, 1750, 1900, 2500, 2250, 2100 \][/tex]

To find the mean area, sum all the values and divide by the number of houses:
[tex]\[ \text{Mean} = \frac{2400 + 1750 + 1900 + 2500 + 2250 + 2100}{6} = \frac{12900}{6} = 2150 \][/tex]

2. Calculate the Squared Deviations from the Mean for Each Area:

Subtract the mean from each area, then square the result:
- For [tex]\(2400\)[/tex]:
[tex]\[ (2400 - 2150)^2 = 250^2 = 62500 \][/tex]
- For [tex]\(1750\)[/tex]:
[tex]\[ (1750 - 2150)^2 = (-400)^2 = 160000 \][/tex]
- For [tex]\(1900\)[/tex]:
[tex]\[ (1900 - 2150)^2 = (-250)^2 = 62500 \][/tex]
- For [tex]\(2500\)[/tex]:
[tex]\[ (2500 - 2150)^2 = 350^2 = 122500 \][/tex]
- For [tex]\(2250\)[/tex]:
[tex]\[ (2250 - 2150)^2 = 100^2 = 10000 \][/tex]
- For [tex]\(2100\)[/tex]:
[tex]\[ (2100 - 2150)^2 = (-50)^2 = 2500 \][/tex]

3. Sum Up the Squared Deviations:

Add all the squared deviations to get the numerator for the variance calculation:
[tex]\[ 62500 + 160000 + 62500 + 122500 + 10000 + 2500 = 420000 \][/tex]

Therefore, the option that represents the numerator in the calculation of variance and standard deviation is:
[tex]\[ \boxed{(250)^2+(-400)^2+(-250)^2+(350)^2+(100)^2+(-50)^2=420,000} \][/tex]

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