quantitative analysis

Excel Formulas

Ages of Nine Children at Forsyth Academy (FA) and Kimberly Park (KP) Elementary Schools
		FA	KP		Bins	Frequency FA	Frequency KP
		6	5		5	0	1
		6	7		6	2	0
		7	7		7	5	7
		7	7		8	2	0								Children at FA are more closely clustered around the mean than those at KP.
		7	7		9	0	1								Any measure of dispersion should be lower for FA than KP.
		7	7
		7	7
		8	7
		8	9
	mean	7	7
	MAD Derrick Boone: Intuitively, any measure of dispersion should be higher for KP because the data are more spread out. However, Mean Absolute Difference (based on the absolute value of how each observation differs from the mean) is the same for FA and KP, which is counterintuitive.	0.44	0.44
	Std Derrick Boone: Intuitively, any measure of dispersion should be higher for KP because the data are more spread out. Std and Var (based on the square of how each observation differs from the mean) are higher for KP than for FA, which follows our intuition.	0.71	1.00
	Var	0.50	1.00
	CV Derrick Boone: The Coefficient of Variation (CV) is higher for KP, which is in line with out intution.	0.10	0.14
															Children at KP are not as closely clustered around the mean as those at FA.
															Any measure of dispersion should be higher for KP than FA.

Frequency FA 5 6 7 8 9 0 2 5 2 0

Age (years)

Count

Frequency KP 5 6 7 8 9 1 0 7 0 1

Age (years)

Count

Manual Calculations

Ages of Nine Children at Forsyth Academy (FA) and Kimberly Park (KP) Elementary Schools
	FA	Ages	xi - avg	|xi - avg|		(xi - avg)2
		6	-1	1		1
		6	-1	1		1
		7	0	0		0
		7	0	0		0
		7	0	0		0
		7	0	0		0
		7	0	0		0
		8	1	1		1
		8	1	1		1
	sum	63	0	4		4
	count	9	9	9		9
	average	7	0	0.44		0.44
	std					0.71
	KP	Ages	xi - avg	|xi - avg|		(xi - avg)2
		9	2	2		4
		7	0	0		0
		7	0	0		0
		7	0	0		0
		7	0	0		0
		7	0	0		0
		7	0	0		0
		7	0	0		0
		5	-2	2		4
	sum	63	0	4		8
	count	9	9	9		9
	average	7	0	0.44		0.89
	Std					1.00