VARIANCE

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Variance = å (X – X )² / N ,

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Where X is the respondent’s answer, X is the Mean or average response,

å is summation or add these squared differences together, and N is the sample size.

The 2001 NSF study of Democratic and Republican grassroots party activists in Mississippi studied the liberal-conservative ideologies of party officials. The calculation of variance for each party follows:

MISSISSIPPPI DEMOCRATS (their mean ideology was 2.69)

X Value and Category Name	f	__ X – X	__ (X – X )^2	__ (X – X )^2 * f
1- Very Liberal	52	1-2.69 = -1.69	2.856	2.856 * 52 = 148.512
2 – Somewhat Liberal	126	2-2.69 = -.69	.476	.476 * 126 = 59.976
3 – Moderate	80	3-2.69 = .31	.096	.096 * 80 = 7.680
4 – Somewhat Conservative	68	4-2.69 = 1.31	1.716	1.716 * 68 = 116.688
5 – Very Conservative	27	5-2.69 = 2.31	5.336	5.336 * 27 = 144.072
	N = 353			Col. Total = 476.928

Variance = 476.928 / 353 = 1.351

MISSISSIPPPI REPUBLICANS (their mean ideology was 4.45)

X Value and Category Name	f	__ X – X	__ (X – X )^2	__ (X – X )^2 * f
1- Very Liberal	2	1-4.45 = -3.45	11.903	11.903 * 2 = 23.806
2 – Somewhat Liberal	5	2-4.45 = -2.45	6.003	6.003 * 5 = 30.015
3 – Moderate	29	3-4.45 = -1.45	2.103	2.103 * 29 = 60.987
4 – Somewhat Conservative	171	4-4.45 = -.45	.203	.203 * 171 = 34.713
5 – Very Conservative	250	5-4.45 = .55	.303	.303 * 250 = 75.750
	N = 457			Col. Total = 225.271

Variance = 225.271 / 457 = .493

Republicans have a lower variance, so they are more united.

SUBGROUP DIFFERENCES:

I also calculated race differences in variance and means for the Democrats. They follow:

White Democrats variance = 1.18. Their mean is 3.01.

Black Democrats variance = 1.32. Their mean is 2.34.