Question

2. Square Footage of Housing The frequency distribution in the next column represents the square footage of a random sample of 500 houses that are owner occupied year round. Approximate the mean and standard deviation square footage.

Answer 1

Square Footage	Cummulative interval improved	Midpoint	Frequency	step deviation (m -A)	frequency* step deviation	(x-mean)	(x-mean)^2	f(x-mean)
0-499	0.5 - 499.5	249.5	5	-2000	-10000	-3690	13616100	68080500
500-999	499.5-999.5	749.5	17	-1500	-25500	-3190	10176100	172993700
1000-1499	999.5-1499.5	1249.5	36	-1000	-36000	-2690	7236100	260499600
1500-1999	1499.5-1999.5	1749.5	121	-500	-60500	-2190	4796100	580328100
2000-2499	1999.5-2499.5	2249.5	119	0	0	-1690	2856100	339875900
2500-2999	2499.5-2999.5	2749.5	81	500	40500	-1190	1416100	114704100
3000-3499	2999.5-3499.5	3249.5	47	1000	47000	-690	476100	22376700
3500-3999	3499.5-3999.5	3749.5	45	1500	67500	-190	36100	1624500
4000-4499	3999.5-4499.5	4249.5	22	2000	44000	310	96100	2114200
4500-4999	4499.5-4999.5	4749.5	7	2500	17500	810	656100	4592700
			500		84500			1567190000
		A=2249.5		mean = 3939.5
		Σfd = 845000	Σf(x-mean)^2 = 1567190000
		N =500		N=500

mean = A + Σfd/N = 2249.5 + 845000/500 = 3939.5 square footage

standard deviation = Square root (Σf(x-mean)^2/n) = Square root (1567190000/500) =

square root (3134380) = 1770.41803