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

Answer 1

Option c is the correct answer which represents the numerator in the calculation of variance and standard deviation.

What are the variance and standard deviation?  

In statistics, variance is a measure of the variation of data from the mean, whereas standard deviation is the measure of the normal distribution of statistical data.

A contractor records the areas, in square feet, of a small sample of houses in a neighborhood to determine data about the neighborhood.

2,400; 1,750; 1,900; 2,500; 2,250; 2,100

we need to find 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  

92416.60

The variance is 84000

The standard deviation is 290

mean = (2400+1750+1900+2500+2250+2100)/6

mean = 2150

Subtract the data values from the mean to get

2400-2150 = 250

1750-2150 = -400

1900-2150 = -250

2500-2150 = 350

2250-2150 = 100

2100-2150 = -50

The differences are 250, -400, -250, 350, 100, -50

Then you square those values and add up the squares

(250)^2 +  (-400)^2 +  (-250)^2 +  (350)^2 +  (100)^2 +  (-50)^2 = 420,000

Hence, option c is the correct answer which represents the numerator in the calculation of variance and standard deviation.

Learn more about variance;

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